Solve ∫ (from 1.5 to 35) of (25+18x) wrt x

$$\int _ { 1.5 } ^ { 35 } ( 25 + 18 x ) d x$$

Evaluate

$$11842.25$$

Solution Steps

Evaluate the indefinite integral first.

$$\int 25+18x\mathrm{d}x$$

Integrate the sum term by term.

$$\int 25\mathrm{d}x+\int 18x\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 25\mathrm{d}x+18\int x\mathrm{d}x$$

Find the integral of 25 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$25x+18\int x\mathrm{d}x$$

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 18 times \frac{x^{2}}{2}.

$$25x+9x^{2}$$

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.

$$25\times 35+9\times 35^{2}-\left(25\times 1.5+9\times 1.5^{2}\right)$$

Simplify.

$$11842.25$$