Solve ∫ (from -1 to 3) of 3(20)left|20-4right| wrt x=

$$\int_{ -1 }^{ 3 } 3(20) \left| 20-4 \right| d x =$$

Evaluate

$$3840$$

Solution Steps

Multiply 3 and 20 to get 60.

$$\int _{-1}^{3}60|20-4|\mathrm{d}x$$

Subtract 4 from 20 to get 16.

$$\int _{-1}^{3}60|16|\mathrm{d}x$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 16 is 16.

$$\int _{-1}^{3}60\times 16\mathrm{d}x$$

Multiply 60 and 16 to get 960.

$$\int _{-1}^{3}960\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int 960\mathrm{d}x$$

Find the integral of 960 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$960x$$

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.

$$960\times 3-960\left(-1\right)$$

Simplify.

$$3840$$