Finding $frac{1}{2pi}int_{0}^{2pi}phi^prime(x) dx$, where $phi(x)=arctanfrac{3cos x}{4(cos x+sin x)}$. Why...
$begingroup$
I'm tasked with the following problem:
Evaluate
$$I_C=frac{1}{2pi}int_{0}^{2pi}left(frac{d}{dtheta}phi(theta)right) dtheta,quadtext{where}; phi(theta)=arctanleft[frac{3cos(theta)}{4(cos(theta)+sin(theta))}right]$$
Am I correct in assuming that this is simply $phi(2pi)-phi(0)$? When I do that I get zero, but when I take the derivative, then evaluate the integral I get -1. How do I use the fundamental theorem of calculus to get the correct answer?
calculus
edited Dec 11 '18 at 9:10
Blue
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
$endgroup$
add a comment |
$begingroup$
I'm tasked with the following problem:
Evaluate
$$I_C=frac{1}{2pi}int_{0}^{2pi}left(frac{d}{dtheta}phi(theta)right) dtheta,quadtext{where}; phi(theta)=arctanleft[frac{3cos(theta)}{4(cos(theta)+sin(theta))}right]$$
Am I correct in assuming that this is simply $phi(2pi)-phi(0)$? When I do that I get zero, but when I take the derivative, then evaluate the integral I get -1. How do I use the fundamental theorem of calculus to get the correct answer?
calculus
edited Dec 11 '18 at 9:10
Blue
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
$endgroup$
add a comment |
$begingroup$
I'm tasked with the following problem:
Evaluate
$$I_C=frac{1}{2pi}int_{0}^{2pi}left(frac{d}{dtheta}phi(theta)right) dtheta,quadtext{where}; phi(theta)=arctanleft[frac{3cos(theta)}{4(cos(theta)+sin(theta))}right]$$
Am I correct in assuming that this is simply $phi(2pi)-phi(0)$? When I do that I get zero, but when I take the derivative, then evaluate the integral I get -1. How do I use the fundamental theorem of calculus to get the correct answer?
calculus
edited Dec 11 '18 at 9:10
Blue
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
$endgroup$
I'm tasked with the following problem:
Evaluate
$$I_C=frac{1}{2pi}int_{0}^{2pi}left(frac{d}{dtheta}phi(theta)right) dtheta,quadtext{where}; phi(theta)=arctanleft[frac{3cos(theta)}{4(cos(theta)+sin(theta))}right]$$
Am I correct in assuming that this is simply $phi(2pi)-phi(0)$? When I do that I get zero, but when I take the derivative, then evaluate the integral I get -1. How do I use the fundamental theorem of calculus to get the correct answer?
calculus
calculus
edited Dec 11 '18 at 9:10
Blue
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
edited Dec 11 '18 at 9:10
Blue
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
edited Dec 11 '18 at 9:10
Blue
48.6k870154
edited Dec 11 '18 at 9:10
Blue
48.6k870154
edited Dec 11 '18 at 9:10
Blue
48.6k870154
48.6k870154
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
asked Dec 10 '18 at 6:49
PeetriusPeetrius
414111
414111
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: what happens at $theta =3pi/4, 7pi/4$? See the graph if required.
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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%2fmath.stackexchange.com%2fquestions%2f3033554%2ffinding-frac12-pi-int-02-pi-phi-primex-dx-where-phix-arctan%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: what happens at $theta =3pi/4, 7pi/4$? See the graph if required.
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
$endgroup$
add a comment |
$begingroup$
Hint: what happens at $theta =3pi/4, 7pi/4$? See the graph if required.
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
$endgroup$
add a comment |
$begingroup$
Hint: what happens at $theta =3pi/4, 7pi/4$? See the graph if required.
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
$endgroup$
Hint: what happens at $theta =3pi/4, 7pi/4$? See the graph if required.
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
edited Dec 11 '18 at 8:40
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
answered Dec 10 '18 at 8:28
Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla
34.4k42871
34.4k42871
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f3033554%2ffinding-frac12-pi-int-02-pi-phi-primex-dx-where-phix-arctan%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
