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)=x2, y=0, x=1, x=5.

Answer 1

624.8 pi

Explanation:

Given that a parabola open up with original as vertex is rotated about x axis

LImits for x are 1 and 5

y = x^2 is the parabola

We have volume when rotated about x axis is

`\pi \int\limits^a_b {y^2} \, dx`

Here lower limit = 1 and higher limit = 5

`\pi \int\limits^5_1 {y^2} \, dx \\=\pi \int\limits^5_1 {x^4} \, dx \\=\pi ((x^5)/(5) )_1^5\\=\pi ((1)/(5) )(5^5-1^5)\\= 624.8 \pi`

Volume generated = 624.8 pi