Solve ∫ (from 0.4 to 0.8) of 0.08/x wrt x

$$\int_{ 0.4 }^{ 0.8 } \frac{ 0.08 }{ x } d x$$

Evaluate

$$\frac{2\ln(2)}{25}\approx 0.055451774$$

Solution Steps

Evaluate the indefinite integral first.

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

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

$$\frac{2\int \frac{1}{x}\mathrm{d}x}{25}$$

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

$$\frac{2\ln(|x|)}{25}$$

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.

$$0.08\ln(|0.8|)-0.08\ln(|0.4|)$$

Simplify.

$$\frac{2\ln(2)}{25}$$