Solve ∫ (from 0 to 4) of (0.083x^3) wrt x

$$\int_{ 0 }^{ 4 } (0.083 { x }^{ 3 } ) d x$$

Evaluate

$$5.312$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{83x^{3}}{1000}\mathrm{d}x$$

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

$$\frac{83\int x^{3}\mathrm{d}x}{1000}$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.

$$\frac{83x^{4}}{4000}$$

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.

$$\frac{83}{4000}\times 4^{4}-\frac{83}{4000}\times 0^{4}$$

Simplify.

$$\frac{664}{125}$$