Solve ∫ (from 1 to 2) of frac{sqrt{pi}}{x}x wrt x

$$\int _ { 1 } ^ { 2 } \frac { \sqrt { \pi } } { x } x d x$$

Evaluate

$$\sqrt{\pi }\approx 1.772453851$$

Solution Steps

Cancel out x and x.

$$\int _{1}^{2}\sqrt{\pi }\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \sqrt{\pi }\mathrm{d}x$$

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

$$\sqrt{\pi }x$$

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.

$$\pi ^{\frac{1}{2}}\times 2-\pi ^{\frac{1}{2}}$$

Simplify.

$$\sqrt{\pi }$$