Answer:
[tex]40.5 \pi[/tex] cubic units
Step-by-step explanation:
Given is a function exponential as
[tex]f(x) =\sqrt{ (x-4)}[/tex]
The region bounded by the above curve, y =0 , x =13 is rotated about x axis.
the intersection point is at x=4
The limits for x are 4 and 13
The volume when rotated through x axis is found by
[tex]\pi\int\limits^b_a {f(x)^2} \, dx[/tex]
Here a = 4 and b =13
volume = [tex]\pi\int\limits^13_(4) x-4} \, dx[/tex]
=[tex]\pi (\frac{x^2 }{2}-4x )\\= \frac{\pi}{2} (153-72)\\= 40.5 \pi[/tex].cubic units
