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

The integral from 0 to 20 of sqrt(5x) is 400/3

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integral from 0 to 20 of sqrt(5x)

\int_{0}^{20} 5 x d x

\frac{400}{3}

Decimal

133.33333 \dots

Solution steps

\int_{0}^{20} 5 x d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int_{0}^{20} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{0}^{20} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{20}

= 5 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{20}

Compute the boundaries:

\frac{80 5}{3}

= 5 \frac{80 5}{3}

Simplify

= \frac{400}{3}

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

\int_{0}^{1} x (1 - x) d x

What is the integral from 0 to 20 of sqrt(5x) ?
The integral from 0 to 20 of sqrt(5x) is 400/3