Solve ∫ (from 5 to 10) of (3x+3) wrt x=

$$\int _ { 5 } ^ { 10 } ( 3 x + 3 ) d x =$$

Evaluate

$$\frac{255}{2}=127.5$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 3x+3\mathrm{d}x$$

Integrate the sum term by term.

$$\int 3x\mathrm{d}x+\int 3\mathrm{d}x$$

Factor out the constant in each of the terms.

$$3\int x\mathrm{d}x+\int 3\mathrm{d}x$$

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

$$\frac{3x^{2}}{2}+\int 3\mathrm{d}x$$

Find the integral of 3 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{3x^{2}}{2}+3x$$

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.

$$\frac{3}{2}\times 10^{2}+3\times 10-\left(\frac{3}{2}\times 5^{2}+3\times 5\right)$$

Simplify.

$$\frac{255}{2}$$