# Volumes of Solids of Revolution - Integration

• Oct 2nd 2009, 01:21 AM
khanim
Volumes of Solids of Revolution - Integration
I hope this in the correct section, admin please move it if its not (Bandit)

Determine the volume generated when the given plane figure is rotated about the y axis

$\displaystyle x^2 - y^2 = 16$

$\displaystyle y=0$ $\displaystyle x=8$

I'm having a problem with the integration part of it (Headbang)
• Oct 2nd 2009, 03:57 AM
mr fantastic
Quote:

Originally Posted by khanim
I hope this in the correct section, admin please move it if its not (Bandit)

Determine the volume generated when the given plane figure is rotated about the y axis

$\displaystyle x^2 - y^2 = 16$

$\displaystyle y=0$ $\displaystyle x=8$

I'm having a problem with the integration part of it (Headbang)

By definition: $\displaystyle V = \pi \int_{y = 0}^{y = 8} x^2 \, dy$.

Substitute $\displaystyle x^2 = 16 + y^2$ into the integral. I don't see where the trouble can be ....?
• Oct 2nd 2009, 05:05 AM
DeMath
Quote:

Originally Posted by mr fantastic
By definition: $\displaystyle V = \pi \int_{y = 0}^{y = 8} x^2 \, dy$.

Substitute $\displaystyle x^2 = 16 + y^2$ into the integral. I don't see where the trouble can be ....?

Maybe do you mean this $\displaystyle V = \pi \int\limits_0^{4\sqrt 3 } {\left( {64 - \left( {16 + {y^2}} \right)} \right)dy}$ ??