Question

I've been having trouble solving this problem for a long time.

I used the variables:
a=1 , b = 2
Height = x^2
Radius : 1+ x
And took the integral of it using the cylindrical shell method.

Answer 1

The radius should be "x - 1" .

The region is revolving around the line x= 1. The radius is distance from this line. So radius varies from 0 to 1 as x goes from 1 to 2.
Therefore , r = x - 1.

Everything else is correct.

Here is the integral solution:


`V = 2\pi \int_1^2 (x-1) x^2 dx \\ \\ = 2\pi \int_1^2 x^3 -x^2 dx \\ \\ = 2\pi |_1^2 ((x^4)/(4) - (x^3)/(3)) \\ \\ =2\pi ((4)/(3) - (-(1)/(12))) \\ \\ =(17\pi)/(6)`