2. Find the area between y^{2} = 4x and 4x – 3y = 4.

NEED SKETCH

For this one, we need to use x dy instead of y dx. Sketch the dA element each way, and you’ll see that it won’t work using dx..

First find the limits:

y^{2} = 3y + 4

y^{2} – 3y – 4 = 0

(y – 4)(y + 1) = 0 y = 4, -1

Now set up the equation for area and solve: