Solve ∫ (from 1 to 9) of (1/2x) wrt x

$$\int_{ 1 }^{ 9 } ( \frac{ 1 }{ 2x } ) d x$$

Evaluate

$$\ln(3)\approx 1.098612289$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{1}{2x}\mathrm{d}x$$

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

$$\frac{\int \frac{1}{x}\mathrm{d}x}{2}$$

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$\frac{\ln(|x|)}{2}$$

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.

$$\frac{1}{2}\ln(|9|)-\frac{1}{2}\ln(|1|)$$

Simplify.

$$\ln(3)$$