Hey there, me and my friends have been trying to solve this double integration problem that we have but seems like we can't find a solution, we would love to hear what you might have to help us!
Here is the question:
∫ ∫D ( xy^2)/2048 dxdy , where D is the limited area in the right halfplane that lays inside the circle x^2+y^2=128 and the curve y^2=8x
the problem with this question is which limits we should have for our integrals,
what we think we should have is for x to be [0, sqrt(128)] and y to be either [-8,8] or [8x,sqrt(128-x^2)] but we dont get the right answer when we do this.
I also attached a picture so you can see where the lines intersect so you maybe understand our reason better for why we would think this. My only guess is that we maybe should try polar coordinates instead as this doesnt seem to work
Here is the question:
∫ ∫D ( xy^2)/2048 dxdy , where D is the limited area in the right halfplane that lays inside the circle x^2+y^2=128 and the curve y^2=8x
the problem with this question is which limits we should have for our integrals,
what we think we should have is for x to be [0, sqrt(128)] and y to be either [-8,8] or [8x,sqrt(128-x^2)] but we dont get the right answer when we do this.
I also attached a picture so you can see where the lines intersect so you maybe understand our reason better for why we would think this. My only guess is that we maybe should try polar coordinates instead as this doesnt seem to work
