Question

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=√x+5, y=0, x=1, x=3.

Answer 1

`14\pi`

Explanation:

We are given:
`f(x) = √(x+5)`

To calculate the desired volume, we need to use the volume property of integral.

`V=\pi\int\limits^3_1(√(x+5))^2dx=\pi\int\limits^3_1(x+5)dx=\pi((x^2)/(2)+5x)|^3_1=\pi((9)/(2)+15-(1)/(2)-5)=14\pi`