DOUBLE INTEGRAL PROBLEM: by first converting to polar coordinates, integrate cos(x^2+y^2) dy dx from x=-2 to 2 from y=0 to sqrt(4-(x^2))

Question

anonymous · Answer

You are able to convert dydx to rdrd(theta). Going back to your trigonometry, what does x^2+y^2 equal? r^2 Your equation is now double integral of rcos(r^2)drd(theta). You will need to change your limits accordingly. (Consider if theta goes from 0 to 2pi or to a different value) also, starting from the origin- imagine r as an arrow that goes outward, the first curve it hits would be the lower limit and the second curve it hits would be the upper limit. Let me know if you need anything clarified!

anonymous · Answer

I am having trouble finding the new limits of integration :(

anonymous · Answer

Remember That Y=sqrt(4-x^2) can be rearranged to  x^2+y^2=4 or r^2=4 or r=2 for the upper limit. The r limits of integration would go from 0 to 2. Is this clear or should I find a better way of explaining it?