What is the integral from 0 to 5 of (10)/(sqrt(x)) ?

The integral from 0 to 5 of (10)/(sqrt(x)) is 20sqrt(5)

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integral from 0 to 5 of (10)/(sqrt(x))

\int_{0}^{5} \frac{10}{x} d x

205

Decimal

44.72135 \dots

Solution steps

\int_{0}^{5} \frac{10}{x} d x

Take the constant out:

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

= 10 \cdot \int_{0}^{5} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{0}^{5}

= 10 [2 x^{\frac{1}{2}}]_{0}^{5}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 10 [2 x]_{0}^{5}

Compute the boundaries:

25

= 10 \cdot 25

Simplify

= 205

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What is the integral from 0 to 5 of (10)/(sqrt(x)) ?
The integral from 0 to 5 of (10)/(sqrt(x)) is 20sqrt(5)