In problem set 8, Problem 2.b), I have parametrised x(r,theta) and y(r,theta). Then I parametrised r and theta in terms of t. I got a huge expression for F and for dr. I get integral from 0 to 1 of F(t)dt. I can't imagine I'm doing it right. Here's the link http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/assignments/ps8.pdf

Question

In problem set 8, Problem 2.b), I have parametrised x(r,theta) and y(r,theta). Then I parametrised r and theta in terms of t. I got a huge expression for F and for dr. I get integral from 0 to 1 of F(t)<r2cos(theta)...,...>dt.
I can't imagine I'm doing it right. Here's the link http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/assignments/ps8.pdf

owlfred · Answer

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anonymous · Answer

You don't need to parametrize x,y for twice. Just set x= a*cos(theta), y= a*sin(theta) , then  dx= -a*sin(theta)*d(theta), dy=a*cos(theta)*d(theta). Then plug all these 4 equations into the M*dx + N*dy in the line integral, where theta ranges from 0 to 2*pai. As a result, what you get now is a simple single-variable definite integral with respect to theta!