Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x = 0, x = 8; about the x-axis V = Sketch the region. Sketch the solid, and a typical disk or washer.

Answer 1

Answer:

Step-by-step explanation:

the region is bounded by

. y = x + 1, y = 0, x = 0, x = 8;

and rotated about x axis.

The limits for x are from 0 to 8

The region is between x+1 and 0

Hence using washer method volume

= $V=\pi\int\limits^8_0 {(x+1)^2-0^2} \, dx \\=\pi*\frac{(x+1)^3}{3}$

substitute limits

V=$\frac{\pi}{3}9^3\\= 243\pi$

cubic units.