Originally Posted by

**momopeaches** This problem involves a change in variable of the limit of integration.

Consider the area bounded by $\displaystyle y=\frac{8x^2}{\sqrt(1-2x^2)}$, y=0, x=0, and x=.5. A definite integral of this area, using x as the variable of integration, is

$\displaystyle \int^x_0 \frac{8x^2}{\sqrt(1-2x^2)}$. The next part of the question says: make the substitution of the form $\displaystyle x = A sin\theta$ to transform the integral so that $\displaystyle \theta$ is the variable of integration.

I'm not sure how to start this one. I thought of simply solving for $\displaystyle \theta$, but I'm don't know how to transform the integrand.