What is the integral from 1 to infinity of pi(1/x)^2 ?

The integral from 1 to infinity of pi(1/x)^2 is pi

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integral from 1 to infinity of pi(1/x)^2

\int_{1}^{\infty} π (\frac{1}{x})^{2} d x

π

Decimal

3.14159 \dots

Solution steps

\int_{1}^{\infty} π (\frac{1}{x})^{2} d x

Compute the indefinite integral:

\int π (\frac{1}{x})^{2} d x = - \frac{π}{x} + C

Compute the boundaries:

\int_{1}^{\infty} π (\frac{1}{x})^{2} d x = 0 - (- π)

= 0 - (- π)

Simplify

= π

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\int_{0}^{t^{4}} u^{3} d u

What is the integral from 1 to infinity of pi(1/x)^2 ?
The integral from 1 to infinity of pi(1/x)^2 is pi