Question

What is the volume of the solid using cylindrical shells of the area enclosed by the curves y=x^(1/3) and y=x^2 rotated about the x-axis?

Answer 1

volume = (2/5)*pi

Explanation:

Volume = piintegration of[ {x^(2/3) - x^4}dx from x = 0 to x = 1]
= pi[ (3/5){x^(5/3) - (1/5)x^5} from x = 0 to x = 1]
= pi[ (3/5){1^(5/3) - (1/5)1^5} - 0]
= pi[ (3/5) - 1/5]
=(2/5)*pi