Question

If you have a region R in the xy plane bounded by y^2=2x and y=x, find the area of R.

Answer 1

I want to mention that this problem is solved using double integrals.

Answer 2

First find the intercepts, so subbing y=x into the first equation. You will find the intercepts at (0,0) and (2,2). So integrating vertical pieces, it's the double integral of dydx, with your bounds for y being from x to sqrt(2x) and your bound for x being from 0 to 2. Solving this integral, you will see its the same thing as doing it as a single integral

Answer 3

Thanks for your prompt answer. I don't quite understand what you mean by integrating vertical pieces?

Answer 4

I'm not very good at explaining this part but I think when you integrate the y, the bounds are not constant, so you have strips that that vary in height. Then you integrate those strips over that over the x boundary which is a constant. If you integrate dxdy first, then you would be integrating horizontal strips vertically