Integration Help Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?Understanding output of multivariable integrationHow do I generate arbitrarily many integration bounds?Getting long complex-valued integrals when simpler real-valued expressions existsymbolic integration of product of hankel function and trignometric functionA Chain rule proof using MathematicaHelp with IntegrationHow to solve this integration?How to get the partial derivative of the inverse functions?Possible bug in integration involving $cos (n phi)$Integration with parameter
Why do we bend a book to keep it straight?
What are the out-of-universe reasons for the references to Toby Maguire-era Spider-Man in ITSV
Do I really need recursive chmod to restrict access to a folder?
Is it cost-effective to upgrade an old-ish Giant Escape R3 commuter bike with entry-level branded parts (wheels, drivetrain)?
How do I find out the mythology and history of my Fortress?
Extracting terms with certain heads in a function
Significance of Cersei's obsession with elephants?
Where are Serre’s lectures at Collège de France to be found?
Do I really need to have a message in a novel to appeal to readers?
Fundamental Solution of the Pell Equation
Would "destroying" Wurmcoil Engine prevent its tokens from being created?
Maximum summed powersets with non-adjacent items
Using audio cues to encourage good posture
What does "lightly crushed" mean for cardamon pods?
Why are there no cargo aircraft with "flying wing" design?
representation of vector and matrix in latex
Is "Reachable Object" really an NP-complete problem?
Is there a kind of relay only consumes power when switching?
Do square wave exist?
For a new assistant professor in CS, how to build/manage a publication pipeline
Does classifying an integer as a discrete log require it be part of a multiplicative group?
Is it ethical to give a final exam after the professor has quit before teaching the remaining chapters of the course?
When the Haste spell ends on a creature, do attackers have advantage against that creature?
Why are the trig functions versine, haversine, exsecant, etc, rarely used in modern mathematics?
Integration Help
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?Understanding output of multivariable integrationHow do I generate arbitrarily many integration bounds?Getting long complex-valued integrals when simpler real-valued expressions existsymbolic integration of product of hankel function and trignometric functionA Chain rule proof using MathematicaHelp with IntegrationHow to solve this integration?How to get the partial derivative of the inverse functions?Possible bug in integration involving $cos (n phi)$Integration with parameter
$begingroup$
So I have to integrate $$fracsin^n xsin^n x + cos^n x$$ and am coding this in Mathematica with
(((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x])))
with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.
I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is
(((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))),
but does not solve it. Anyone know how to help or fix this??
calculus-and-analysis
New contributor
$endgroup$
add a comment |
$begingroup$
So I have to integrate $$fracsin^n xsin^n x + cos^n x$$ and am coding this in Mathematica with
(((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x])))
with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.
I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is
(((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))),
but does not solve it. Anyone know how to help or fix this??
calculus-and-analysis
New contributor
$endgroup$
1
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using(Sin^2)[x]
when that syntax is incorrect, you should instead write it asSin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago
add a comment |
$begingroup$
So I have to integrate $$fracsin^n xsin^n x + cos^n x$$ and am coding this in Mathematica with
(((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x])))
with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.
I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is
(((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))),
but does not solve it. Anyone know how to help or fix this??
calculus-and-analysis
New contributor
$endgroup$
So I have to integrate $$fracsin^n xsin^n x + cos^n x$$ and am coding this in Mathematica with
(((Sin^n)[x])/(((Sin^n)[x]) + ((Cos^n)[x])))
with the bounds $0$ and $pi/2,$ where $n$ takes on various integer values.
I programmed the problem so that $n=1$ then $n=2$, etc...but every time I try to get the output, I only get back the integration symbol. For example, if I program $n=2$ and then do the integration command- the output is
(((Sin^2)[x])/(((Sin^2)[x]) + ((Cos^2)[x]))),
but does not solve it. Anyone know how to help or fix this??
calculus-and-analysis
calculus-and-analysis
New contributor
New contributor
edited 1 hour ago
Michael E2
151k12203482
151k12203482
New contributor
asked 4 hours ago
EmmaEmma
62
62
New contributor
New contributor
1
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using(Sin^2)[x]
when that syntax is incorrect, you should instead write it asSin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago
add a comment |
1
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using(Sin^2)[x]
when that syntax is incorrect, you should instead write it asSin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago
1
1
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using
(Sin^2)[x]
when that syntax is incorrect, you should instead write it as Sin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using
(Sin^2)[x]
when that syntax is incorrect, you should instead write it as Sin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
This works for me:
Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),x,0,Pi/2],n,1,5]
And it gives the output Pi/4,Pi/4,Pi/4,Pi/4,Pi/4.
$endgroup$
1
$begingroup$
Recommend that you add aPlot
to make it easier to understand why the result is a constant.
$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
add a comment |
$begingroup$
Perhaps you're writing your function in the wrong format Emma. The following works fine:
n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),x, 0, π/2]
π/4
$endgroup$
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
add a comment |
$begingroup$
A common trick (see this Math.SE post:
ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, x_, a_, b_, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, x, a, b, opts]
symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), x, 0, [Pi]/2]]
(* [Pi]/4 *)
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195438%2fintegration-help%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This works for me:
Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),x,0,Pi/2],n,1,5]
And it gives the output Pi/4,Pi/4,Pi/4,Pi/4,Pi/4.
$endgroup$
1
$begingroup$
Recommend that you add aPlot
to make it easier to understand why the result is a constant.
$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
add a comment |
$begingroup$
This works for me:
Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),x,0,Pi/2],n,1,5]
And it gives the output Pi/4,Pi/4,Pi/4,Pi/4,Pi/4.
$endgroup$
1
$begingroup$
Recommend that you add aPlot
to make it easier to understand why the result is a constant.
$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
add a comment |
$begingroup$
This works for me:
Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),x,0,Pi/2],n,1,5]
And it gives the output Pi/4,Pi/4,Pi/4,Pi/4,Pi/4.
$endgroup$
This works for me:
Table[Integrate[Sin[x]^n/(Sin[x]^n+Cos[x]^n),x,0,Pi/2],n,1,5]
And it gives the output Pi/4,Pi/4,Pi/4,Pi/4,Pi/4.
edited 4 hours ago
answered 4 hours ago
Kevin AusmanKevin Ausman
32417
32417
1
$begingroup$
Recommend that you add aPlot
to make it easier to understand why the result is a constant.
$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
add a comment |
1
$begingroup$
Recommend that you add aPlot
to make it easier to understand why the result is a constant.
$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
1
1
$begingroup$
Recommend that you add a
Plot
to make it easier to understand why the result is a constant.$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Recommend that you add a
Plot
to make it easier to understand why the result is a constant.$endgroup$
– Bob Hanlon
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
$begingroup$
Good suggestion. Editing.
$endgroup$
– Kevin Ausman
4 hours ago
add a comment |
$begingroup$
Perhaps you're writing your function in the wrong format Emma. The following works fine:
n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),x, 0, π/2]
π/4
$endgroup$
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
add a comment |
$begingroup$
Perhaps you're writing your function in the wrong format Emma. The following works fine:
n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),x, 0, π/2]
π/4
$endgroup$
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
add a comment |
$begingroup$
Perhaps you're writing your function in the wrong format Emma. The following works fine:
n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),x, 0, π/2]
π/4
$endgroup$
Perhaps you're writing your function in the wrong format Emma. The following works fine:
n = 2;
Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n),x, 0, π/2]
π/4
edited 3 hours ago
m_goldberg
88.8k873200
88.8k873200
answered 4 hours ago
amator2357amator2357
1437
1437
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
add a comment |
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
$begingroup$
I believe you have the parentheses in the wrong place relative to the original question. Right idea for the solution, though.
$endgroup$
– Kevin Ausman
4 hours ago
1
1
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
$begingroup$
Yes, just realized that, thanks for pointing it out.
$endgroup$
– amator2357
4 hours ago
add a comment |
$begingroup$
A common trick (see this Math.SE post:
ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, x_, a_, b_, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, x, a, b, opts]
symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), x, 0, [Pi]/2]]
(* [Pi]/4 *)
$endgroup$
add a comment |
$begingroup$
A common trick (see this Math.SE post:
ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, x_, a_, b_, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, x, a, b, opts]
symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), x, 0, [Pi]/2]]
(* [Pi]/4 *)
$endgroup$
add a comment |
$begingroup$
A common trick (see this Math.SE post:
ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, x_, a_, b_, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, x, a, b, opts]
symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), x, 0, [Pi]/2]]
(* [Pi]/4 *)
$endgroup$
A common trick (see this Math.SE post:
ClearAll[symmetrizeIntegrate];
SetAttributes[symmetrizeIntegrate, HoldAll];
symmetrizeIntegrate[Integrate[f_, x_, a_, b_, opts___]] :=
Integrate[(f + (f /. x -> a + b - x))/2, x, a, b, opts]
symmetrizeIntegrate[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), x, 0, [Pi]/2]]
(* [Pi]/4 *)
answered 1 hour ago
Michael E2Michael E2
151k12203482
151k12203482
add a comment |
add a comment |
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f195438%2fintegration-help%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Hello! It seems that you haven't included any code. Can you please include that here in the post? Based on your textual description my guess is that you are using
(Sin^2)[x]
when that syntax is incorrect, you should instead write it asSin[x]^2
$endgroup$
– enano9314
4 hours ago
$begingroup$
Related: math.stackexchange.com/questions/82489/…
$endgroup$
– Michael E2
1 hour ago