Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^(1/3) and y=x/7, about the line x=−4

Answer 1

Intersection: x^1/3 = x/7; x = 0 and x = 7^3/2.

By shell method V = 2π∫₀^{7^3/2}(x + 4)(x^1/3 - x/7)dx = 850.92

To evaluate integral we use TI-84