I ran into some trouble with some integrals that use polar coordinates.
Sounds fair!
....
The region for integration is a triangle which I thought was a little weird. I think the r limits start from 0 to something (I called it b in the integral below), but I think the
limits are
.
So, without the final r limit, I have
.
My problem with this one is that the region of integration is not a circle centred at the origin but rather the point
. I am aware that the region is a semi circle. For this reason, are the
limits
?
Are the r limits
?
However, the integrand is going to be
.
So overall, I get that the integral should be
.
Clearly the r limits are incorrect!
From here, I decided to put
into the upper limit of the double integral:
.
Is this integral the correct one to evaluate?