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

The integral from 0 to 5 of pi(25-25x^2) is -pi 2750/3

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

\int_{0}^{5} π (25 - 25 x^{2}) d x

- π \frac{2750}{3}

Decimal

- 2879.79326 \dots

Solution steps

\int_{0}^{5} π (25 - 25 x^{2}) 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 - 25 x^{2} 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 d x - \int_{0}^{5} 25 x^{2} d x)

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

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

= π (125 - \frac{3125}{3})

Simplify

π (125 - \frac{3125}{3}) : - π \frac{2750}{3}

= - π \frac{2750}{3}

f (x) = 8 e^{x} cos (x), (0, 8)

\frac{d}{d t} (\frac{t}{t ^{2} + y ^{2}})

x \to 5 lim (3 x^{2} + 5)

\frac{d}{d x} (\frac{2}{3} x^{2})

\frac{d}{d x} (\frac{c ^{6} - x ^{6}}{c ^{6} + x ^{6}})

What is the integral from 0 to 5 of pi(25-25x^2) ?
The integral from 0 to 5 of pi(25-25x^2) is -pi 2750/3