Question

What is the integral of `|x|`?

Answer 1

Let's take `a<0` and `b>0`, then `int_a^b |x|dx = int_a^0-xdx + int_0^bxdx = int_0^-axdx + int_0^bxdx = [1/2x^2]_0^-a +[1/2x^2]_0^b= 1/2(-a)^2+1/2b^2 = 1/2a^2+1/2b^2`