What is the integral from 0 to 1 of pi(x^2-x^6) ?

The integral from 0 to 1 of pi(x^2-x^6) is pi 4/21

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

\int_{0}^{1} π (x^{2} - x^{6}) d x

π \frac{4}{21}

Decimal

0.59839 \dots

Solution steps

\int_{0}^{1} π (x^{2} - x^{6}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \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

= π (\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}

= π (\frac{1}{3} - \frac{1}{7})

Join

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

= π \frac{4}{21}

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