Solve ∫ (from 4 to 10) of (0.6x)(0.6x) wrt x

$$\int_{ 4 }^{ 10 } (0.6x)(0.6x) d x$$

Evaluate

$$112.32$$

Solution Steps

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

$$\int _{4}^{10}0.6x^{2}\times 0.6\mathrm{d}x$$

Multiply 0.6 and 0.6 to get 0.36.

$$\int _{4}^{10}0.36x^{2}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{9x^{2}}{25}\mathrm{d}x$$

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

$$\frac{9\int x^{2}\mathrm{d}x}{25}$$

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}.

$$\frac{3x^{3}}{25}$$

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.

$$\frac{3}{25}\times 10^{3}-\frac{3}{25}\times 4^{3}$$

Simplify.

$$\frac{2808}{25}$$