Area between two curves (1 Viewer)

[RoXaH]

Calculate the area of the region enclosed by the line y = x+1 and the parabola y= x^2/4 - 2

 

[Uncle]

1.
It really helps to sketch the region and it is always done whether you are evaluating integrals in polar coordinates or double integrals so you know what you are dealing with.

2.
As you can see, the two functions intersect at two points, equate them both and solve for the two intercepts.

Intercepts:

Spoiler

x = - 2 and x = 6

3.
To solve for areas bounded between two functions, the usual option is to go and integrate the top function minus the bottom function.
Use your two intercepts as the limits of integration.
That's why sketching the two functions help you decide which one is top and which one is bottom.

Answer:

Spoiler

64/3