What is the integral from 1 to 3 of (x^3)/(sqrt(x)) ?

The integral from 1 to 3 of (x^3)/(sqrt(x)) is (54sqrt(3)-2)/7

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integral from 1 to 3 of (x^3)/(sqrt(x))

\int_{1}^{3} \frac{x ^{3}}{x} d x

\frac{54 3 - 2}{7}

Decimal

13.07582 \dots

Solution steps

\int_{1}^{3} \frac{x ^{3}}{x} d x

Simplify

\frac{x ^{3}}{x} : x^{\frac{5}{2}}

= \int_{1}^{3} x^{\frac{5}{2}} d x

Apply the Power Rule

: [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{3}

= [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{3}

Compute the boundaries:

\frac{54 3}{7} - \frac{2}{7}

= \frac{54 3}{7} - \frac{2}{7}

Simplify

= \frac{54 3 - 2}{7}

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What is the integral from 1 to 3 of (x^3)/(sqrt(x)) ?
The integral from 1 to 3 of (x^3)/(sqrt(x)) is (54sqrt(3)-2)/7