Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question

y=x+1, y=0, x=0, x=2 ; about the x-axis.

a) v=

b) Sketch the region.

c) Sketch the solid, and a typical disk or washer.

Answer 1

V = π∫₀²(x + 1)²dx = π(x + 1)³/3₀²= π(9 - 1/3) = 26/3π = 27.23