Question

Question #f7ed1

Answer 1

`int_{-1}^{1} abs(x) dx = 1`

Explanation:

`f(x)` is a piecewise function.

`f(x) = {(x if x >= 0),(-x if x < 0) ]`

Hence, separate the integral into 2 parts.

`int_{-1}^{1} f(x) dx = int_{-1}^{0} f(x) dx + int_{0}^{1} f(x) dx`

`= int_{-1}^{0} (-x) dx + int_{0}^{1} x dx`

`= [-x^2/2]_{-1}^0 + [x^2/2]_0^1`

`= 1/2 + 1/2`

`= 1`