Question

g (3 points)Set up but do no solve the integral required to calculate the volume formed by rotating the region bounded by f(x) = 1/x,g(x) = 1/x^3, andx= 2, andx= 4 around they-axis. Also draw a picture of the region (non-revolved).

Answer 1

Hello,

Explanation:

`\displaystyleV=2*\pi*\int\limits^4_2 {((1)/(x)-(1)/(x^3) )*x } \, dx \\=2*\pi*\int\limits^4_2 {(1-(1)/(x^2) ) } \, dx \\=2*\pi* [x+(1)/(x)]^4_2\\\\\boxed{V=(7\pi)/(2)}\\`