Question

Find the volume generated by revolving about the x-axis the regions bounded by the following graphs: y = sqrt 1+x x = 0 x = 10

Answer 1

Answer:

60 pi cubic units.

Step-by-step explanation:

Given that a region bounded by

$y = \sqrt{1+x} \\x = 0\\ x = 10$

is revolved around x axis.

To find the volume of generated solid

we know that when a curve is rotated form x=a to x=b around x axis

Volume V = $\int_a^b \pi y^2 dx$

Substitute a=0 , b =10 and $y^2 =1+x$

we have

Volume = $\int_0^{10} \pi (1+x) dx\\= \pi (x+\frac{x^2}{2)} \\=\pi(10+50)\\= 60\pi$

Hence volume would be 60 pi cubic units.