Question

Determine the volume of the solid formed when the region enclosed by the curve y=√x, the x-axis, and the line x = 4, is revolved about the line x = 4.

Answer 1

$V=\pi. \int _a^b f(x) ^2 dx$

$V= \pi. \int_0^4\sqrt x) ^2 dx$

$V=\pi. \int_0^4 x dx$

$V=\pi. [x^2/2]_0^4$

$V= \pi. [4^2/2] - \pi. [0^2/2]$

$V= 8\pi$

$V= 8 ×3.142$

$V=25.136$ cubic units