# Is This Right For Volume of Solids?

• April 27th 2009, 06:37 PM
summermagic
Is This Right For Volume of Solids?
Let R be the shaded region bounded by the graph of $y=lnx$ and the line $y=x-2$.

Find the volume of the solid generated when R is rotated about the horizontal line y=-3.

Is this the correct integral for the volume?

$\pi \int^{0.15859434}_{3.1461932} [{(lnx)^2-(x-2)^2}]dx$
• April 27th 2009, 06:53 PM
Shyam
Quote:

Originally Posted by summermagic
Let R be the shaded region bounded by the graph of $y=lnx$ and the line $y=x-2$.

Find the volume of the solid generated when R is rotated about the horizontal line y=-3.

Is this the correct integral for the volume?

$\pi \int^{0.15859434}_{3.1461932} [{(lnx)^2-(x-2)^2}]dx$

$
=\pi \int^{0.15859434}_{3.1461932} [{(lnx+3)^2-(x-2+3)^2}]dx
$

$=\pi \int^{0.15859434}_{3.1461932} [{(lnx+3)^2-(x+1)^2}]dx
$

Finish it.