A solid is obtained by rotating the curve about its

Question

Question: For a positive constant a, consider the curve

y = √((x³)/(a - x)), 0 ≤ x < a

(a) Using a computer algebra system, show that for 0 ≤ t

x = a sin² t, y = a sin³ t/cos t

(b) A solid is obtained by rotating the curve about its asymptote at x = a. Use horizontal slicing to write an integral in terms of x and y that represents the volume of this solid.

(c) Use part (a) to substitute in the integral for both x and y in terms of t. Use a computer algebra system or trigonometric identities to calculate the volume of the solid.