What is the integral from 0 to 1 of pi(x-x^{10}) ?

The integral from 0 to 1 of pi(x-x^{10}) is pi 9/22

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integral from 0 to 1 of pi(x-x^{10})

\int_{0}^{1} π (x - x^{10}) d x

π \frac{9}{22}

Decimal

1.28519 \dots

Solution steps

\int_{0}^{1} π (x - x^{10}) 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 - x^{10} 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 d x - \int_{0}^{1} x^{10} d x)

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

\int_{0}^{1} x^{10} d x = \frac{1}{11}

= π (\frac{1}{2} - \frac{1}{11})

Join

\frac{1}{2} - \frac{1}{11} : \frac{9}{22}

= π \frac{9}{22}

What is the integral from 0 to 1 of pi(x-x^{10}) ?
The integral from 0 to 1 of pi(x-x^{10}) is pi 9/22