What is the integral from 0 to 3 of sqrt(3x) ?

The integral from 0 to 3 of sqrt(3x) is 6

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integral from 0 to 3 of sqrt(3x)

\int_{0}^{3} 3 x d x

6

Solution steps

\int_{0}^{3} 3 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int_{0}^{3} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{0}^{3} x d x

Apply the Power Rule

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

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

Compute the boundaries:

23

= 3 \cdot 23

Simplify

= 6

\frac{d}{d x} (2 - 3 x^{2})

\frac{\partial}{\partial y} (x^{\frac{3}{4}} y^{\frac{1}{4}})

y = x^{2}, y = 4

f (t) = e^{5 t s i n (2 t)}

x \to 2 lim (3 x^{4} + 4 x^{3} - x + 2)

What is the integral from 0 to 3 of sqrt(3x) ?
The integral from 0 to 3 of sqrt(3x) is 6