Solve ∫ (from -1 to 3) of 3(4)left|4-4right| wrt x=

$$\int_{ -1 }^{ 3 } 3(4) \left| 4-4 \right| d x =$$

Evaluate

$$0$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\int _{-1}^{3}12|4-4|\mathrm{d}x$$

Subtract 4 from 4 to get 0.

$$\int _{-1}^{3}12|0|\mathrm{d}x$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$\int _{-1}^{3}12\times 0\mathrm{d}x$$

Multiply 12 and 0 to get 0.

$$\int _{-1}^{3}0\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int 0\mathrm{d}x$$

Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$0$$

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.

$$0+0$$

Simplify.

$$0$$