Find the volume of the solid between the planes

Question

Find the volume of the solid above the region D={(x,y): 0<=x<= √63, <=y<= 63-x²} and between the planes z=63-y, z=0.

Answer 1

V = ∫₀^√63 ∫₀^{63-x^2} ∫₀^63-y d z d y d x

∫₀^√63 ∫₀^{63-x^2} [ 63−y ] d y d x

∫₀^√63 { [ 63y −y²/2 ] |₀^{63-x^2} } d x

∫₀^√63 [ 63( 63−x² ) −(1/2) ( 63−x² )² ] d x = [ 23814√7 ] / 5