Calculus help on practice final!!!?

Question

can anyone please help me set up the washer method for the following equation

find the volume of the solid generated by revolving the plane region bounded by the graphs of x^2 = y - 2 and 2y - x -2 = 0 about the line y =3 with x =0, x=1

thank you

Answer 1

x² = y - 2

y = x² + 2

2y - x - 2 = 0

y = (x+2)/2

washer method

V = π ∫(outer radius)² - (inner radius)²

graph the two functions and you'll see:

outer radius = 3 - (x+2)/2

inner radius = 3 - (x²+2)

so,

V = π ∫[3 - (x+2)/2]² - [3 - (x²+2)]² dx from 0 to 1

integrate and compute the limits and you'll get V = 51π/20