Question

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

Answer 1

Answer:

5.333 \pi

Step-by-step explanation:

Given is a function exponential as

$f(x) = \frac{x^2}{4}$

The region bounded by the above curve, y =0 , x=4  is rotated about x axis.

The intersection of curve with x axis is at x=0

The limits for x are 0 and 4

The volume when rotated through x axis is found by

$\pi\int\limits^b_a {f(x)^2} \, dx$

Here a = 0 and b =4

volume = $\pi\int\limits^4_(0) \frac{x^2}{4} \, dx$

=$\pi (\frac{x^3} }{12} )\\= \frac{\pi}{12} (64-0)\\= 5.333 \pi$