What is the integral from 0 to 1 of pi(3x^2-3x^6) ?

The integral from 0 to 1 of pi(3x^2-3x^6) is pi 4/7

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integral from 0 to 1 of pi(3x^2-3x^6)

\int_{0}^{1} π (3 x^{2} - 3 x^{6}) d x

π \frac{4}{7}

Decimal

1.79519 \dots

Solution steps

\int_{0}^{1} π (3 x^{2} - 3 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} 3 x^{2} - 3 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} 3 x^{2} d x - \int_{0}^{1} 3 x^{6} d x)

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

\int_{0}^{1} 3 x^{6} d x = \frac{3}{7}

= π (1 - \frac{3}{7})

Join

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

= π \frac{4}{7}

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What is the integral from 0 to 1 of pi(3x^2-3x^6) ?
The integral from 0 to 1 of pi(3x^2-3x^6) is pi 4/7