What is the integral from 1 to 3 of pi(1/x)^2 ?

The integral from 1 to 3 of pi(1/x)^2 is (2pi)/3

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integral from 1 to 3 of pi(1/x)^2

\int_{1}^{3} π (\frac{1}{x})^{2} d x

\frac{2 π}{3}

Decimal

2.09439 \dots

Solution steps

\int_{1}^{3} π (\frac{1}{x})^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{1}^{3} (\frac{1}{x})^{2} d x

Simplify

(\frac{1}{x})^{2} : \frac{1}{x ^{2}}

= π \cdot \int_{1}^{3} \frac{1}{x ^{2}} d x

Apply the Power Rule

: [- \frac{1}{x}]_{1}^{3}

= π [- \frac{1}{x}]_{1}^{3}

Compute the boundaries:

\frac{2}{3}

= π \frac{2}{3}

Simplify

= \frac{2 π}{3}

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What is the integral from 1 to 3 of pi(1/x)^2 ?
The integral from 1 to 3 of pi(1/x)^2 is (2pi)/3