What is the integral from 0 to 1 of (\sqrt[3]{1+7x}) ?

The integral from 0 to 1 of (\sqrt[3]{1+7x}) is 45/28

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integral from 0 to 1 of (\sqrt[3]{1+7x})

\frac{45}{28}

Decimal

1.60714 \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{1}{7} [\frac{3}{4} u^{\frac{4}{3}}]_{1}^{8}

Compute the boundaries:

\frac{45}{4}

= \frac{1}{7} \cdot \frac{45}{4}

Simplify

= \frac{45}{28}

What is the integral from 0 to 1 of (\sqrt[3]{1+7x}) ?
The integral from 0 to 1 of (\sqrt[3]{1+7x}) is 45/28