Urgent(due in 2 hours)!! calculating volume of Cartesian Coordinates and Polar Coordinates!?

Your box for f in the polar coordinates form is NOT correct. It should be √(64 - r^2). You can do the θ integration first, which gives 2π. So you're down to

......4
4π ∫ r (64 - r²)^½ dr
.....0

Use the substitution u = 64 - r². Then
du = -2r dr
-½ du =r dr
When r = 0, u = 64; when r = 4, u = 48

and the integral becomes

......48
2π ∫ -u^½ du
....64

which is the same as

......64
2π ∫ u^½ du
....48

You can finish.