What is the integral from 1 to 9 of (2/(sqrt(x))) ?

The integral from 1 to 9 of (2/(sqrt(x))) is 8

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integral from 1 to 9 of (2/(sqrt(x)))

\int_{1}^{9} (\frac{2}{x}) d x

8

Solution steps

\int_{1}^{9} \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_{1}^{9} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{1}^{9}

= 2 [2 x^{\frac{1}{2}}]_{1}^{9}

Apply radical rule:

= 2 [2 x]_{1}^{9}

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

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What is the integral from 1 to 9 of (2/(sqrt(x))) ?
The integral from 1 to 9 of (2/(sqrt(x))) is 8