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2 years ago

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

Mathematics

1 answer:

Maslowich2 years ago

4 0

Answer:

16 pi cubic units

Step-by-step explanation:

Given that a region is bounded by

$f(x)=√x, y=0, x=1, x=4$

And the region is rotated about x axis.

We can find that here radius would be y value and height would be dx

So volume would be as follows:

If f(x) is rotated about x axis volume

= $\pi \int\limits^b_a {y^2} \, dx \\=\pi \int\limits^4_1 {x} \, dx\\=\pi *x^2 ^4_1\\= \pi*16-1\\=15\pi$

cubic units.

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