How do you evaluate the integral of absolute value of (x - 5) from 0 to 10 by finding area?

First you find the integral by using the property the integral of x^n (where n is a number) = (x^ (n+1)) / (n+1)

So in this case:

abs (x-5) = x^n (where n=1) - 5x^m (where m=0)

so when you solve for it, you get

=abs ([ (x^ (1+1)) / (1+1) ] - [5 (x^ (0+1)) / (0+1) ]) from 0 to 10

= abs (.5x^2 - 5x) from 0 to 10

then plug in the top value, x=10, and subtract the bottom value, x=0, from it:

=abs (.5 (10^2) - 5 (10)) - abs (.5 (0) - 5 (0))

=0 - 0

=0