You know me well sir. I already was there deriving them, now most of them I can see what to do. But one is alluding me . Now I haven't given it much time butHey mathstud, you know what might be fun?. Go to the link I posted above and actually derive the solutions they give for the integrals. You have probably done that already.
Some of them are probably very challenging.
Ok my first move was to do the obvious double integral
So we have
Now rewriting this as (this is so people who aren't super accustomed to double integrals can see what I am doing)
From here it is obvious that this region is a rectangle, so Fubini's Theorem applies
Now this inner integral is bothering me, I cannot seem to get it in the eight minutes I have tried
Letting -no go
I also tried some crazy thing where I let
And found that the integral I want is a constant difference from