Solve ∫ (from 0.1 to 0.2) of 3*10^4/x wrt x

$$\int _ { 0.1 } ^ { 0.2 } \frac { 3 \times 10 ^ { 4 } } { x } d x$$

Evaluate

$$30000\ln(2)\approx 20794.415416798$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{3\times 10^{4}}{x}\mathrm{d}x$$

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

$$3\times 10^{4}\int \frac{1}{x}\mathrm{d}x$$

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

$$3\times 10^{4}\ln(|x|)$$

Simplify.

$$30000\ln(|x|)$$

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.

$$30000\ln(|0.2|)-30000\ln(|0.1|)$$

Simplify.

$$30000\ln(2)$$