Intersection curve: Parameterization, length.
up vote
0
down vote
favorite
I'm stuck on this problem and i'm not really sure how to proceed to resolve it:
Consider the curve $C$ of intersection between the plane:
$z=2-x$
and the cylinder:
$x^2+y^2=1$
$a)$ Find the parameters of $C$
$b)$ Find the length of curve $C$
I did this:
$a)$ :
$x(t)=cos(t)$
$y(t)=sin(t)$
$z(t)=2-cos(t)$
$b)$ :
$|r'(t)|=√[1+sin^2(t)]$
And the length is given by:
$∫|r'(t)|$ from $t=0..2π$
But I'm not sure. If correct, how do I evaluate that integral?
(Solution given by WolframAlpha: https://www3.wolframalpha.com/Calculate/MSP/MSP335110dde1b3ca040a51000037i327f275aadg38?MSPStoreType=image/gif&s=27)
calculus multivariable-calculus parametrization
asked Nov 25 at 19:29
Pedro Sierra
43
add a comment |
up vote
0
down vote
favorite
I'm stuck on this problem and i'm not really sure how to proceed to resolve it:
Consider the curve $C$ of intersection between the plane:
$z=2-x$
and the cylinder:
$x^2+y^2=1$
$a)$ Find the parameters of $C$
$b)$ Find the length of curve $C$
I did this:
$a)$ :
$x(t)=cos(t)$
$y(t)=sin(t)$
$z(t)=2-cos(t)$
$b)$ :
$|r'(t)|=√[1+sin^2(t)]$
And the length is given by:
$∫|r'(t)|$ from $t=0..2π$
But I'm not sure. If correct, how do I evaluate that integral?
(Solution given by WolframAlpha: https://www3.wolframalpha.com/Calculate/MSP/MSP335110dde1b3ca040a51000037i327f275aadg38?MSPStoreType=image/gif&s=27)
calculus multivariable-calculus parametrization
asked Nov 25 at 19:29
Pedro Sierra
43
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm stuck on this problem and i'm not really sure how to proceed to resolve it:
Consider the curve $C$ of intersection between the plane:
$z=2-x$
and the cylinder:
$x^2+y^2=1$
$a)$ Find the parameters of $C$
$b)$ Find the length of curve $C$
I did this:
$a)$ :
$x(t)=cos(t)$
$y(t)=sin(t)$
$z(t)=2-cos(t)$
$b)$ :
$|r'(t)|=√[1+sin^2(t)]$
And the length is given by:
$∫|r'(t)|$ from $t=0..2π$
But I'm not sure. If correct, how do I evaluate that integral?
(Solution given by WolframAlpha: https://www3.wolframalpha.com/Calculate/MSP/MSP335110dde1b3ca040a51000037i327f275aadg38?MSPStoreType=image/gif&s=27)
calculus multivariable-calculus parametrization
asked Nov 25 at 19:29
Pedro Sierra
43
I'm stuck on this problem and i'm not really sure how to proceed to resolve it:
Consider the curve $C$ of intersection between the plane:
$z=2-x$
and the cylinder:
$x^2+y^2=1$
$a)$ Find the parameters of $C$
$b)$ Find the length of curve $C$
I did this:
$a)$ :
$x(t)=cos(t)$
$y(t)=sin(t)$
$z(t)=2-cos(t)$
$b)$ :
$|r'(t)|=√[1+sin^2(t)]$
And the length is given by:
$∫|r'(t)|$ from $t=0..2π$
But I'm not sure. If correct, how do I evaluate that integral?
(Solution given by WolframAlpha: https://www3.wolframalpha.com/Calculate/MSP/MSP335110dde1b3ca040a51000037i327f275aadg38?MSPStoreType=image/gif&s=27)
calculus multivariable-calculus parametrization
calculus multivariable-calculus parametrization
asked Nov 25 at 19:29
Pedro Sierra
43
asked Nov 25 at 19:29
Pedro Sierra
43
edited Nov 25 at 20:17
asked Nov 25 at 19:29
Pedro Sierra
43
asked Nov 25 at 19:29
Pedro Sierra
43
asked Nov 25 at 19:29
Pedro Sierra
43
43
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3013278%2fintersection-curve-parameterization-length%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
