# Thread: Volumes of Solids of Revolution - Integration

1. ## Volumes of Solids of Revolution - Integration

I hope this in the correct section, admin please move it if its not

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

2. Originally Posted by khanim
I hope this in the correct section, admin please move it if its not

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