What is the integral from 0 to 4 of 2/(sqrt(x)) ?

The integral from 0 to 4 of 2/(sqrt(x)) is 8

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integral from 0 to 4 of 2/(sqrt(x))

\int_{0}^{4} \frac{2}{x} d x

8

Solution steps

\int_{0}^{4} \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_{0}^{4} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{0}^{4}

= 2 [2 x^{\frac{1}{2}}]_{0}^{4}

Apply radical rule:

= 2 [2 x]_{0}^{4}

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

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What is the integral from 0 to 4 of 2/(sqrt(x)) ?
The integral from 0 to 4 of 2/(sqrt(x)) is 8