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

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

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

\int_{1}^{2} π (\frac{1}{x})^{2} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Simplify

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

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

Apply the Power Rule

: [- \frac{1}{x}]_{1}^{2}

= π [- \frac{1}{x}]_{1}^{2}

Compute the boundaries:

\frac{1}{2}

= π \frac{1}{2}

Simplify

= \frac{π}{2}

\int_{5}^{11} \frac{16}{x - 1} d x

\int_{0}^{1} (x^{2} - x)^{2} d x

\frac{d}{d x} (\frac{tan ( x )}{x})

n = 0 \sum \infty \frac{n}{3 ^{n}}

f (x) = arccos (2 x)

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