Answer:
5.333 \pi
Step-by-step explanation:
Given is a function exponential as
[tex]f(x) = \frac{x^2}{4}[/tex]
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
[tex]\pi\int\limits^b_a {f(x)^2} \, dx[/tex]
Here a = 0 and b =4
volume = [tex]\pi\int\limits^4_(0) \frac{x^2}{4} \, dx[/tex]
=[tex]\pi (\frac{x^3} }{12} )\\= \frac{\pi}{12} (64-0)\\= 5.333 \pi[/tex]
