The boundaries:
x = 0, y = 8; y = 0, √x³ = = 8, x = 4
[tex]A= \int\limits^4_0 {(8- x^{3/2}) } \, dx = \\ =8 x - 2 \sqrt{ x^{5} }/5= \\ 8*4-64/5 =19.2 [/tex]
[tex]V = \int\limits^4_0 { \pi (8 - x^{3/2}) } \, dx = \\ = \pi \int\limits^0_4 {(64 - 16 * 2 \sqrt{ x^{5} /5} + x^{4}/4) \, dx = [/tex]
= π ( 64 x - 16 * 2 *√x^5 + x^4 / 4 ) =
= π ( 320 - 1024/5 + 64 ) = 179.2 π
