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 10/21

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integral from 0 to 1 of (x^2+x^6)

\int_{0}^{1} (x^{2} + x^{6}) d x

\frac{10}{21}

Decimal

0.47619 \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{10}{21}

= \frac{10}{21}

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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 10/21