Find the Area between $ y=\sin \left(\frac{\pi x}{2}\right)$ and $y=x^2$
So I know how to solve this specific case, but one thing I'm not sure of let's say we have:
$y=x^2$ and $\:y=\sin \:\left(ax\right)\:$
How do I find where they intercept? $$\:x^2=\sin \:\left(ax\right)\:$$
This type of equation ($x^2=\sin(ax)$) is usually only solvable using numerical methods. However, in this case, you can compute two fixed points easily ($x=0$ and $x=1$). Then comparing the derivatives of the two functions can help you proving that these two points are the only intersections between the two graphs.