What is the integral from 0 to 1 of (x^3-x^4) ?

The integral from 0 to 1 of (x^3-x^4) is 1/20

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integral from 0 to 1 of (x^3-x^4)

\int_{0}^{1} (x^{3} - x^{4}) d x

\frac{1}{20}

Decimal

0.05

Solution steps

\int_{0}^{1} x^{3} - 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^{3} d x - \int_{0}^{1} x^{4} d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

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

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

Simplify

\frac{1}{4} - \frac{1}{5} : \frac{1}{20}

= \frac{1}{20}

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What is the integral from 0 to 1 of (x^3-x^4) ?
The integral from 0 to 1 of (x^3-x^4) is 1/20