Question

find the area of the shaded region bounded by y=x^2-4x and y=x-4 @zepdrix

Answer 1

It always helps if you can DRAW the region, so you know which one is on top, and which on bottom.

This one is a little tricky, since the first equation is a tough to graph if you don't remember your algebra.

Let's put it in standard form a second.
Completing the square gives us,\[\large y=x^2-4x+4-4 \qquad \rightarrow \qquad y=(x-2)^2-4\]

Answer 2

set the two equations equal to each other to find where they intersect so:
x^2-4x=x-4
x^2-5x+4=0
(x-4)(x-1)=0
now u have the two x values 1 and 4 which are the upper and lower limit of the integral requires to find the shaded area so intergrate from there