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Popular Calculus >

integral from 0 to 1 of x^2-x^6

Solution

\int_{0}^{1} x^{2} - x^{6} d x

Solution

\frac{4}{21}

+1

Decimal

0.19047 \dots

Solution steps

\int_{0}^{1} x^{2} - x^{6} 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^{2} d x - \int_{0}^{1} x^{6} d x

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

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= \frac{1}{3} - \frac{1}{7}

Simplify

\frac{1}{3} - \frac{1}{7} : \frac{4}{21}

= \frac{4}{21}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of x^2-x^6 ?
The integral from 0 to 1 of x^2-x^6 is 4/21