What is the integral from 0 to 1 of (1-\sqrt[4]{x}) ?

The integral from 0 to 1 of (1-\sqrt[4]{x}) is 1/5

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integral from 0 to 1 of (1-\sqrt[4]{x})

\int_{0}^{1} (1 - 4 x) d x

\frac{1}{5}

Decimal

0.2

Solution steps

\int_{0}^{1} 1 - 4 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} 1 d x - \int_{0}^{1} 4 x d x

\int_{0}^{1} 1 d x = 1

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

= 1 - \frac{4}{5}

Simplify

1 - \frac{4}{5} : \frac{1}{5}

= \frac{1}{5}

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What is the integral from 0 to 1 of (1-\sqrt[4]{x}) ?
The integral from 0 to 1 of (1-\sqrt[4]{x}) is 1/5