Another Curved Surface Area Problem

[harrietstowe]

Homework Statement

Find the area of the part of the cylinder y^2+z^2=a^2 that lies inside the cylinder x^2 +y^2 = a^2

Homework Equations

The Attempt at a Solution

So the first thing I did was I solved for z from the first equation to get z = Sqrt[a^2-y^2]. I took the partial derivative of z with respect to x to get 0 and the partial derivative with respect to y which is -y/Sqrt[a^2-y^2]
So you integrate over Sqrt[(-y/Sqrt[a^2-y^2] )^2 + 1] = a * sqrt[1/(a^2-y^2)]
I need help finding the boundaries for the double integral
Thanks

 

[Quinzio]

Your boundaries will go from a certain $$x_0$$ to a certain $$x_1$$.
And those "x"s will be a function of "?"
Now guess where you'll take that "?"

Anyway, it seems you have some difficulties managing the whole thing.

Start with something simpler:
- a cylinder $$y^2+z^2=a^2$$

bounded by two planes $$x=a, \ x = -a$$

Find this area, of course not using the classic methods, but using the same method you were trying before.