What is the integral from 1 to 4 of 1/(sqrt(7x)) ?

The integral from 1 to 4 of 1/(sqrt(7x)) is -sqrt(1/7)+3/(sqrt(7))

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integral from 1 to 4 of 1/(sqrt(7x))

\int_{1}^{4} \frac{1}{7 x} d x

- \frac{1}{7} + \frac{3}{7}

Decimal

0.75592 \dots

Solution steps

\int_{1}^{4} \frac{1}{7 x} d x

Apply Integration By Parts

: [\frac{x}{7} - \int - \frac{1}{2 7 x ^{\frac{1}{2}}} d x]_{1}^{4}

= [\frac{x}{7} - \int - \frac{1}{2 7 x ^{\frac{1}{2}}} d x]_{1}^{4}

\int - \frac{1}{2 7 x ^{\frac{1}{2}}} d x = - \frac{1}{7} x

= [\frac{x}{7} - (- \frac{1}{7} x)]_{1}^{4}

Simplify

= [\frac{x}{7} + \frac{1}{7} x]_{1}^{4}

Compute the boundaries:

- \frac{1}{7} + \frac{3}{7}

= - \frac{1}{7} + \frac{3}{7}

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What is the integral from 1 to 4 of 1/(sqrt(7x)) ?
The integral from 1 to 4 of 1/(sqrt(7x)) is -sqrt(1/7)+3/(sqrt(7))