Solve ∫ (from 0 to 8) of (-5.33x+4x)(-0.083x) wrt x

$$\int_{ 0 }^{ 8 } (-5.33x+4x)(-0.083x) d x$$

Evaluate

$$\frac{176624}{9375}\approx 18.839893333$$

Solution Steps

Combine -5.33x and 4x to get -1.33x.

$$\int _{0}^{8}-1.33x\left(-0.083\right)x\mathrm{d}x$$

Multiply -1.33 and -0.083 to get 0.11039.

$$\int _{0}^{8}0.11039xx\mathrm{d}x$$

Multiply x and x to get x^{2}.

$$\int _{0}^{8}0.11039x^{2}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{11039x^{2}}{100000}\mathrm{d}x$$

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{11039\int x^{2}\mathrm{d}x}{100000}$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{11039x^{3}}{300000}$$

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.

$$\frac{11039}{300000}\times 8^{3}-\frac{11039}{300000}\times 0^{3}$$

Simplify.

$$\frac{176624}{9375}$$