I ran into some trouble with some integrals that use polar coordinates.
Sounds fair!Change the following cartesian integrals into an equivalent polar integral. Then evaluate the polar integral.
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 ?2).
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?