Question

The area bounded by the curve y = 2x^2-x^3 and line y=0 is rotated around the y-axis. The volume of the resulting structure can be expressed as V = a(pi)/b, where a and b are coprime positive integers. What is the value of a + b?

Answer 1

Using shells:
v = ∫[0,2] 2πrh dx
where r = x and h = y = 2x^2 - x^3
v = 2π∫[0,2] 2x^3 - x^4 dx
piece of cake from here on

Answer 2

16/5=21