I ran into some trouble with some integrals that use polar coordinates.

Sounds fair!(Clapping)Quote:

Change the following cartesian integrals into an equivalent polar integral. Then evaluate the polar integral.

....(Angry)Quote:

1).

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 ?Quote:

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?