+69 Find the volume of the solid formed by revolving the region bound by y𝑦=x^3, y=3 and x= 0
about the line y=4
+129852 The outer radius = 4 - x^3 Outer radius squared = 16 - 8x^3 + x^6
The inner radius = 4 - 3 = 1 Inner radius squared = 1
The volume is given by
3√4
pi * ∫ (Outer radius)^2 - (Inner radius)^2 dx
0
3√4
pi * ∫ 16 -8x^3 + x^6 - 1 dx
0
3√4
pi * ∫ 15 -8x^3 + x^6 dx =
0
pi * [ 15(3√4) - 2(3√4)^4 + (3√4)^7/7 ] ≈ 14.74 pi units^3
