Question

how do you find the areas bounded between the two curves x+y^2=4 and y=x+2

Answer 1

You probably know how to integrate a function with respect to the variable y. If you rearrange your second equation to x = y-2 and your first equation to x = -y^2 + 4, so that both equations are given in terms of x as functions of y, then you can proceed to integrate. WolframAlpha provides a good visualization of the area you are trying to find through integration. http://www.wolframalpha.com/input/?i=x%2By%5E2%3D4%2C+y+%3D+x%2B2

Answer 2

first find points of intersection by equating bouth functions: x=-y^2+4and x=y-2