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

The integral from 0 to 5 of sqrt(5x) is 50/3

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integral from 0 to 5 of sqrt(5x)

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

\frac{50}{3}

Decimal Notation

16.66666 \dots

Solution steps

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{10 5}{3}

= 5 \frac{10 5}{3}

Simplify

= \frac{50}{3}

y = x, (64, 8)

\frac{12 s}{12 s - 30 s ^{2}}

\frac{d y}{d x} = \frac{( e ^{y} )}{x y}

\frac{1 - 5 t}{4 + t}

\int sin (8 x) cos (8 x) d x

What is the integral from 0 to 5 of sqrt(5x) ?
The integral from 0 to 5 of sqrt(5x) is 50/3