Equivalence of the washer and shell methods for finding volume Let f be differentiable and increasing on the interval a ≤x ≤b with a>0, and suppose that f has a differentiable inverse, f^-1 Revolve about the y -axis the region bounded by the graph of f and the lines x=a and y=f(b) to generate a solid. Then the values of the integrals given by the washer and shell methods for the volume have identical values: ∫f(a)^f(b) π((f^-1(y))^2-a^2) d y=∫a^b 2 πx(f(b)-f(x)) d x To prove this equality, defin