What is the integral from 0 to 7 of sqrt(7x) ?

The integral from 0 to 7 of sqrt(7x) is 98/3

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integral from 0 to 7 of sqrt(7x)

\int_{0}^{7} 7 x d x

\frac{98}{3}

Solution steps

\int_{0}^{7} 7 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int_{0}^{7} 7 x d x

Take the constant out:

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

= 7 \cdot \int_{0}^{7} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{7}

= 7 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{7}

Compute the boundaries:

\frac{14 7}{3}

= 7 \frac{14 7}{3}

Simplify

= \frac{98}{3}

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What is the integral from 0 to 7 of sqrt(7x) ?
The integral from 0 to 7 of sqrt(7x) is 98/3