The question is : find the volume of the region bounded by the paraboloid z=1-4(x^2+y^2) and the xy plane. The answer to this question is 7pi/2. I have tried it but my answer comes out to be pi/8. The integration is correct i have checked with Mathematica, i think i have messed up the limits, maybe.

I took the limits for z from 0 to 1-4r^2, for r from 0 to 1/2 and for theta from 0 to 2pi.

Need help to figure out which one is incorrect.