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

Question

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



y=6-3/2x, y=0, x=1, x=2 ; about the x-axis

V=?

sketch the region

sketch the solid and typical disk or washer

thank you in advance for any help

Answer 1

By disk Method volume V = π∫₁²(6 - 3/2x)²dx = π(-2/3)(1/3)(6 - 3/2x)³₁² = π(-2/9)(27 - 729/8)= 57π/4 = 44.768