# Math Help - riemann sums and definite integral represeting are of region

1. ## riemann sums and definite integral represeting are of region

I have to find the remain sum the the integral of the area between the curves of y=x and y=sqrt(x) with horizontal slices. not sure how to do it, i know it would be the area under y=sqrt(x) minus the area under y=x but not sure how to do it. Thanks for the help!

2. If you solve both equation, you will get the points of intersection as (0,0) and (1,1)

Now So simply integrate $\int (\sqrt(x) - x )dx$ with in limit $x = 0$ to $x= 1$

3. And yes, above solution was for verticle slices. For horizontal slices you have to integrate with respect to y.
So integrate $y - y^2$ wrt y with in same limits y = 0 to y= 1