What is the integral from 3 to 4 of sqrt(3/x) ?

The integral from 3 to 4 of sqrt(3/x) is 4sqrt(3)-6

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integral from 3 to 4 of sqrt(3/x)

\int_{3}^{4} \frac{3}{x} d x

43 - 6

Decimal

0.92820 \dots

Solution steps

\int_{3}^{4} \frac{3}{x} d x

Apply Integration By Parts

: [\frac{3}{x} x - \int - \frac{3}{2 x ^{\frac{1}{2}}} d x]_{3}^{4}

= [\frac{3}{x} x - \int - \frac{3}{2 x ^{\frac{1}{2}}} d x]_{3}^{4}

\int - \frac{3}{2 x ^{\frac{1}{2}}} d x = - 3 x

= [\frac{3}{x} x - (- 3 x)]_{3}^{4}

Simplify

= [\frac{3}{x} x + 3 x]_{3}^{4}

Compute the boundaries:

43 - 6

= 43 - 6

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What is the integral from 3 to 4 of sqrt(3/x) ?
The integral from 3 to 4 of sqrt(3/x) is 4sqrt(3)-6