Intersection curve: Parameterization, length.
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
63
add a comment |
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
63
add a comment |
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
63
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
63
asked Nov 25 at 19:29
Pedro Sierra
63
edited Nov 25 at 20:17
asked Nov 25 at 19:29
Pedro Sierra
63
asked Nov 25 at 19:29
Pedro Sierra
63
asked Nov 25 at 19:29
Pedro Sierra
63
63
add a comment |
add a comment |
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