What is the integral from 0 to 4 of x 3/16 sqrt(x) ?

The integral from 0 to 4 of x 3/16 sqrt(x) is 12/5

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integral from 0 to 4 of x 3/16 sqrt(x)

\int_{0}^{4} x \frac{3}{16} x d x

\frac{12}{5}

Decimal Notation

2.4

Solution steps

\int_{0}^{4} x \frac{3}{16} x d x

Take the constant out:

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

= \frac{3}{16} \cdot \int_{0}^{4} x x d x

Simplify

x x : x^{\frac{3}{2}}

= \frac{3}{16} \cdot \int_{0}^{4} x^{\frac{3}{2}} d x

Apply the Power Rule

: [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{4}

= \frac{3}{16} [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{4}

Compute the boundaries:

\frac{64}{5}

= \frac{3}{16} \cdot \frac{64}{5}

Simplify

= \frac{12}{5}

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What is the integral from 0 to 4 of x 3/16 sqrt(x) ?
The integral from 0 to 4 of x 3/16 sqrt(x) is 12/5