Solve ∫ (from 2 to 3) of x-2 wrt x

$$\int_{ 2 }^{ 3 } x-2 d x$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Evaluate the indefinite integral first.

$$\int x-2\mathrm{d}x$$

Integrate the sum term by term.

$$\int x\mathrm{d}x+\int -2\mathrm{d}x$$

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}.

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

Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x^{2}}{2}-2x$$

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.

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

Simplify.

$$\frac{1}{2}$$