What is the integral from 0 to 5 of pi(25x^2-x^4) ?

The integral from 0 to 5 of pi(25x^2-x^4) is pi 1250/3

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integral from 0 to 5 of pi(25x^2-x^4)

\int_{0}^{5} π (25 x^{2} - x^{4}) d x

π \frac{1250}{3}

Decimal

1308.99693 \dots

Solution steps

\int_{0}^{5} π (25 x^{2} - x^{4}) d x

Take the constant out:

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

= π \cdot \int_{0}^{5} 25 x^{2} - x^{4} 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}^{5} 25 x^{2} d x - \int_{0}^{5} x^{4} d x)

\int_{0}^{5} 25 x^{2} d x = \frac{3125}{3}

\int_{0}^{5} x^{4} d x = 625

= π (\frac{3125}{3} - 625)

Join

\frac{3125}{3} - 625 : \frac{1250}{3}

= π \frac{1250}{3}

What is the integral from 0 to 5 of pi(25x^2-x^4) ?
The integral from 0 to 5 of pi(25x^2-x^4) is pi 1250/3