I need help with integral please!

Question

Evaluate the integral 

Options:

1. -1
2. 1
3. 0
4. 2

Answer 1

Whenever we see an absolute value inside of an integral, we should check to see if the function inside the absolute value ever switches sign.

In this case x = 0 is between the limits of integration. So we can break the integral up at that point using the piecewise definition of absolute value

|x| = { x if x > 0

{ -x if x < 0

∫2|x|dx = ∫-2xdx + ∫2xdx = -x^2 (from -1 to 0) + x^2 (from 0 to 1) = 2