What is the integral from 0 to 5 of pi(25-y^2) ?

The integral from 0 to 5 of pi(25-y^2) is pi 250/3

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integral from 0 to 5 of pi(25-y^2)

\int_{0}^{5} π (25 - y^{2}) d y

π \frac{250}{3}

Decimal

261.79938 \dots

Solution steps

\int_{0}^{5} π (25 - y^{2}) d y

Take the constant out:

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

= π \cdot \int_{0}^{5} 25 - y^{2} 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}^{5} 25 d y - \int_{0}^{5} y^{2} d y)

\int_{0}^{5} 25 d y = 125

\int_{0}^{5} y^{2} d y = \frac{125}{3}

= π (125 - \frac{125}{3})

Join

125 - \frac{125}{3} : \frac{250}{3}

= π \frac{250}{3}

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What is the integral from 0 to 5 of pi(25-y^2) ?
The integral from 0 to 5 of pi(25-y^2) is pi 250/3