What is the integral from 0 to 3.5 of \sqrt[3]{3x+4} ?

The integral from 0 to 3.5 of \sqrt[3]{3x+4} is 7.25215…

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integral from 0 to 3.5 of \sqrt[3]{3x+4}

7.25215 \dots

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: [\frac{3}{4} u^{\frac{4}{3}}]_{4}^{14.5}

= \frac{1}{3} [\frac{3}{4} u^{\frac{4}{3}}]_{4}^{14.5}

Simplify

= 0.33333 \dots [0.75 u^{\frac{4}{3}}]_{4}^{14.5}

Compute the boundaries:

21.75647 \dots

= 0.33333 \dots \cdot 21.75647 \dots

Simplify

= 7.25215 \dots

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What is the integral from 0 to 3.5 of \sqrt[3]{3x+4} ?
The integral from 0 to 3.5 of \sqrt[3]{3x+4} is 7.25215…