How do I integrate these functions?

noobishnoob

New member
Hi,

I am currently working on two separate problems that involve the integration of sin(x2) and er2 with respect to r.

As you can see in the image, the question asks to evalute the double integral using polar coordinates.

Since r=sqrt(x2+y2), the integral becomes sin(r2) and er2. But how do I go ahead with this? It looks like a fairly simple integration, but in my experience it did not turn out to be so.

I have tried integrating this by parts and gone around in circles where the result has to be integrated by parts again and again. I don't seem to recognise any integration method of solving it.

Any advice would be appreciated, thanks.

Jomo

Elite Member
Can you please show us your work so we can see where you are having problems.
Also we really prefer one problem per post.

noobishnoob

New member
Can you please show us your work so we can see where you are having problems.
Also we really prefer one problem per post.
Yeah well it's technically just one problem once I figure out how to do the integral cuz the two parts are pretty much the same thing.

Also here are my workings fr part (a), I dont know how to proceed from here.

Dr.Peterson

Elite Member
Were you taught how to convert a double integral in Cartesian coordinates to polar? Are you aware that dxdy and drdθ are not the same thing? This is what Jomo already referred to.