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

16.66666 \dots

Solution steps

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

Apply radical rule:

n ab = n a n b,

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

= 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}

d er i v a t i v e \frac{1 - 5 t}{4 + t}

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

\frac{d}{d x} (sec^{2} (x) d x)

(6 - 10 y + e^{- 5 x}) d x - 2 d y = 0

t an g e n t y = sec (x), (\frac{π}{3}, 2)

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