Question 66 for GR9768
Posted: Tue Oct 14, 2008 4:15 pm
66. The line integral [x^2 dy -2y dx] over the circle x^2+y^2=9.
Now I tried using Greene's theorem on this but got bogged down when doing the double integral.
M = -2y
N = x^2
Integral of 2x + 2 dA.
First integrate with respect to y with limits +/- Root(9-x^2)
Then you get the integral from -3 to 3 of:
4(x+1)Root(9-x^2) <--- I stopped here.
Instead of using Greeneās theorem I started over parameterizing the equation in terms of t and then solving it directly using a few trig substitutions along the way (answer was 18pi). I was wondering what you guys think the best way to tackle this problem is?
Now I tried using Greene's theorem on this but got bogged down when doing the double integral.
M = -2y
N = x^2
Integral of 2x + 2 dA.
First integrate with respect to y with limits +/- Root(9-x^2)
Then you get the integral from -3 to 3 of:
4(x+1)Root(9-x^2) <--- I stopped here.
Instead of using Greeneās theorem I started over parameterizing the equation in terms of t and then solving it directly using a few trig substitutions along the way (answer was 18pi). I was wondering what you guys think the best way to tackle this problem is?