Solve ∫ _{-sqrt{2}}^sqrt{2}left|xright| wrt x

$$\int_{ - \sqrt{ 2 } }^{ \sqrt{ 2 } } \left| x \right| d x$$

Evaluate

$$2$$

Solution Steps

Evaluate the indefinite integral first.

$$\int |x|\mathrm{d}x$$

Simplify.

$$\frac{x|x|}{2}$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\frac{1}{2}\times 2^{\frac{1}{2}}|2^{\frac{1}{2}}|-\frac{1}{2}\left(-1\right)\times 2^{\frac{1}{2}}|-2^{\frac{1}{2}}|$$

Simplify.

$$2$$