# Areas Under a Curve

1. Apr 4, 2015

### FuturEngineer

Find the area of the regions shown in the figures.

These are the graphs used :

y = x^2
x = 2 Sin ^2 (y)

I know that I need to set the two equations equal to each other in order to find the points of intersection, but I run into some trouble when trying to simplify it for y.

This is what I tried

Since y=x^2
Sqrt.(y)= x

So now I have
x= Sqrt.(y)
x= 2 Sin ^2 (y)

Sqrt.(y) - 2 Sin ^2 (y) = 0

So based on the graph that I am given in the book I can't really tell which is the top or right curve to subtract the bottom or left curve.

After this step I would square both sides and be left with (Sqrt.(y) -2 Sin(^2y)^2) = 0, but I am not sure if that is allowed. Not sure on how to proceed from here. I would appreciate some help. Thanks!

2. Apr 5, 2015

### Svein

Hint: $cos(2y)=1-2sin^{2}(y)$. Rearrange and find y as a function of x.