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

The integral from 1 to 2 of sqrt(2/x) is 4-2sqrt(2)

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integral from 1 to 2 of sqrt(2/x)

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

4 - 22

Decimal Notation

1.17157 \dots

Solution steps

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

Apply Integration By Parts

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

= [\frac{2}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}}} d x]_{1}^{2}

\int - \frac{1}{2 x ^{\frac{1}{2}}} d x = - 2 x

= [\frac{2}{x} x - (- 2 x)]_{1}^{2}

Simplify

= [\frac{2}{x} x + 2 x]_{1}^{2}

Compute the boundaries:

4 - 22

= 4 - 22

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What is the integral from 1 to 2 of sqrt(2/x) ?
The integral from 1 to 2 of sqrt(2/x) is 4-2sqrt(2)