I have a Calc 3 homework due this evening, and one question is causing me trouble. The question is: Verify that Green's Theorem is true for the vector field F = (y^2-7y)i + (2xy+2x)j where C is the circle x^2+y^2=1. (C is the curve to integrate on.)
I set my vector function r=cos(t)i + sin(t)j where 0 < t < 2pi. Then dr= (-sint(t)dt, cos(t)dt). F = (cos^2(t)-7cos(t), -2sin(t)cos(t)-2sin(t)). Is this all right?
I evaluated the line integral from 0-2pi of F dot dr, and it came out to be zero. Then I evaluated the double integral from Green's theorem (dQ/dx) - (dP/dy), with the limits being 0 < y < 1 and 0 < x < sqareroot(1-y^2), and I got 9pi/4. If I'm verifying Green's theorem, the answers from these two integrals should be equal, but they're not. What did I do wrong?
Thanks so much.
2006-12-11
02:38:52
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3 answers
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Anonymous
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Science & Mathematics
➔ Mathematics