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PolarNik [594]
3 years ago
12

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

Mathematics
1 answer:
lana66690 [7]3 years ago
3 0

Answer:

40.5 \pi cubic units

Step-by-step explanation:

Given is a function exponential as

f(x) =\sqrt{ (x-4)}

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

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

Here a = 4 and b =13

volume = \pi\int\limits^13_(4) x-4} \, dx

=\pi (\frac{x^2 }{2}-4x )\\= \frac{\pi}{2} (153-72)\\= 40.5 \pi.cubic units

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