Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. 2x = y2, x = 0, y = 5; about the y-axis

Answer 1

USING THE METHOD OF CYLINDRICAL SHELLS

V= 2π ∫₀^25/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units

USING THE WASHER METHOD

V = ∫₀⁵ π (1/4) y⁴ d y = 625π/ 4 cubic units