What is the integral from 0 to 49 of 8/(sqrt(x)) ?

The integral from 0 to 49 of 8/(sqrt(x)) is 112

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integral from 0 to 49 of 8/(sqrt(x))

\int_{0}^{49} \frac{8}{x} d x

112

Solution steps

\int_{0}^{49} \frac{8}{x} d x

Take the constant out:

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

= 8 \cdot \int_{0}^{49} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{0}^{49}

= 8 [2 x^{\frac{1}{2}}]_{0}^{49}

Apply radical rule:

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

= 8 [2 x]_{0}^{49}

Compute the boundaries:

14

= 8 \cdot 14

Simplify

= 112

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What is the integral from 0 to 49 of 8/(sqrt(x)) ?
The integral from 0 to 49 of 8/(sqrt(x)) is 112