What is the integral from 4 to 25 of 2/(sqrt(x)) ?

The integral from 4 to 25 of 2/(sqrt(x)) is 12

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integral from 4 to 25 of 2/(sqrt(x))

\int_{4}^{25} \frac{2}{x} d x

12

Solution steps

\int_{4}^{25} \frac{2}{x} d x

Take the constant out:

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

= 2 \cdot \int_{4}^{25} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{4}^{25}

= 2 [2 x^{\frac{1}{2}}]_{4}^{25}

Apply radical rule:

= 2 [2 x]_{4}^{25}

Compute the boundaries:

6

= 2 \cdot 6

Simplify

= 12

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What is the integral from 4 to 25 of 2/(sqrt(x)) ?
The integral from 4 to 25 of 2/(sqrt(x)) is 12