Question

Evaluate the integral ∫ |x|dx limit from -1 to 1?

Answer 1

`int_-1^1|x|dx = 1`

Explanation:

You define the`f(x)=|x|`, which is same as defining
`f(x)=-x, x<0` and `f(x)=x, x>=0` at the same time
So you integral is `int_-1^1f(x)dx = int_-1^0-xdx + int_0^1xdx`
`=[-x^2/2]_-1^0 + [x^2/2]_0^1 = 0-(-1/2) + 1/2 - 0 = 1`