What is the integral from 4 to 16 of (3sqrt(x)) ?

The integral from 4 to 16 of (3sqrt(x)) is 112

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integral from 4 to 16 of (3sqrt(x))

\int_{4}^{16} (3 x) d x

112

Solution steps

\int_{4}^{16} 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_{4}^{16} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{4}^{16}

= 3 [\frac{2}{3} x^{\frac{3}{2}}]_{4}^{16}

Compute the boundaries:

\frac{112}{3}

= 3 \cdot \frac{112}{3}

Simplify

= 112

\frac{d}{d x} (\frac{( x - y )}{( x + y )})

\int x sin (\frac{x ^{2}}{2}) d x

\int \frac{2}{7 x} d x

\frac{d y}{d x} = \frac{x}{49 y}

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = 0

What is the integral from 4 to 16 of (3sqrt(x)) ?
The integral from 4 to 16 of (3sqrt(x)) is 112