# Thread: Area of a Surface of Revolution

1. ## Area of a Surface of Revolution

Calculate the area when $\frac{x^2}{4}+\frac{y^2}{2}=1$ is rotated around the y-axis.

This is the formula. $A_y =2\pi\int_a^b x \sqrt{1+\left(\frac{dx}{dy}\right)^2} \, dy$ But when I solve for y, I get a ±. Should I just take the +version?

2. ## Re: Area of a Surface of Revolution

Replacing y by -y will just change dx/dy to -dx/dy and that is squared in your formula. So it really doesn't matter whether you use "y" or "-y".

3. ## Re: Area of a Surface of Revolution

Attempt:

$\frac{dx(y)}{dy} = -2y \centerdot (1 - \frac{y^2}{2})^{-1/2}$

and

$\left({\frac{dx(y)}{dy}}\right)^2 = \frac{4y^2}{1-\frac{y^2}{2}}$

4. ## Re: Area of a Surface of Revolution

I have narrowed this down to finding the primitive of $\sqrt{2+y^2}$ but I'm stuck there.