What is the integral from 0 to 1 of pi(y^2-y^4) ?

The integral from 0 to 1 of pi(y^2-y^4) is pi 2/15

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integral from 0 to 1 of pi(y^2-y^4)

\int_{0}^{1} π (y^{2} - y^{4}) d y

π \frac{2}{15}

Decimal

0.41887 \dots

Solution steps

\int_{0}^{1} π (y^{2} - y^{4}) d y

Take the constant out:

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

= π \cdot \int_{0}^{1} y^{2} - y^{4} d y

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} y^{2} d y - \int_{0}^{1} y^{4} d y)

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

\int_{0}^{1} y^{4} d y = \frac{1}{5}

= π (\frac{1}{3} - \frac{1}{5})

Join

\frac{1}{3} - \frac{1}{5} : \frac{2}{15}

= π \frac{2}{15}

What is the integral from 0 to 1 of pi(y^2-y^4) ?
The integral from 0 to 1 of pi(y^2-y^4) is pi 2/15