What is the integral from 0 to 1 of sqrt(x)-x/4 ?

The integral from 0 to 1 of sqrt(x)-x/4 is 13/24

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integral from 0 to 1 of sqrt(x)-x/4

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

\frac{13}{24}

Decimal Notation

0.54166 \dots

Solution steps

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

\int_{0}^{1} x d x = \frac{2}{3}

\int_{0}^{1} \frac{x}{4} d x = \frac{1}{8}

= \frac{2}{3} - \frac{1}{8}

Simplify

\frac{2}{3} - \frac{1}{8} : \frac{13}{24}

= \frac{13}{24}

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What is the integral from 0 to 1 of sqrt(x)-x/4 ?
The integral from 0 to 1 of sqrt(x)-x/4 is 13/24