# Thread: Volume of revolution help...

1. ## Volume of revolution help...

The region bounded by the curve y = x^2 + 1, the x-axis, the y-axis and the line x = 2 is rotated completely about the x-axis. Find, in terms of $\displaystyle \pi$, the volume of the solid formed.

Using x = 2, the lines should meet at y = 2^2 + 1 = 5. And the vertex is probably at 1, we have the integral limits of 1 and 5.

Volume of the revolution is given by:
$\displaystyle \int_a^b \pi y^2 dy$

$\displaystyle \int_1^5 \pi (y-1) dy = \pi [\frac{1}{2} y^2 - y]$

Using the above doesn't give me the correct answer, so I probably am not doing it right.

2. Originally Posted by struck
The region bounded by the curve y = x^2 + 1, the x-axis, the y-axis and the line x = 2 is rotated completely about the x-axis. Find, in terms of $\displaystyle \pi$, the volume of the solid formed.

Using x = 2, the lines should meet at y = 2^2 + 1 = 5. And the vertex is probably at 1, we have the integral limits of 1 and 5.

Volume of the revolution is given by:
$\displaystyle \int_a^b \pi y^2 dy$

$\displaystyle \int_1^5 \pi (y-1) dy = \pi [\frac{1}{2} y^2 - y]$

Using the above doesn't give me the correct answer, so I probably am not doing it right.
rotation about the x-axis using the disk method ...

$\displaystyle V = \pi \int_0^2 (x^2+1)^2 \, dx$