Solve ∫ (from 1 to 2) of pi1/x^2 wrt x

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

Evaluate

$$\frac{\pi }{2}\approx 1.570796327$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \frac{\pi }{x^{2}}\mathrm{d}x$$

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

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

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}.

$$\pi \left(-\frac{1}{x}\right)$$

Simplify.

$$-\frac{\pi }{x}$$

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.

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

Simplify.

$$\frac{\pi }{2}$$