What is the integral from 0 to 5 of (sqrt(x))/4 ?

The integral from 0 to 5 of (sqrt(x))/4 is (5sqrt(5))/6

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integral from 0 to 5 of (sqrt(x))/4

\int_{0}^{5} \frac{x}{4} d x

\frac{5 5}{6}

Decimal Notation

1.86338 \dots

Solution steps

\int_{0}^{5} \frac{x}{4} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{5} x d x

Apply the Power Rule

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

= \frac{1}{4} [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{5}

Compute the boundaries:

\frac{10 5}{3}

= \frac{1}{4} \cdot \frac{10 5}{3}

Simplify

= \frac{5 5}{6}

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\int_{1}^{4} \frac{x}{1 + x} d x

What is the integral from 0 to 5 of (sqrt(x))/4 ?
The integral from 0 to 5 of (sqrt(x))/4 is (5sqrt(5))/6