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

The integral from-5 to 5 of pi(25-x^2) is pi 500/3

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

\int_{- 5}^{5} π (25 - x^{2}) d x

π \frac{500}{3}

Decimal Notation

523.59877 \dots

Solution steps

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

\int_{- 5}^{5} 25 d x = 250

\int_{- 5}^{5} x^{2} d x = \frac{250}{3}

= π (250 - \frac{250}{3})

Join

250 - \frac{250}{3} : \frac{500}{3}

= π \frac{500}{3}

\int e^{x} e^{x + 1} d x

x \to 6 lim (\frac{x - 6}{∣ x - 6 ∣})

n = 1 \sum \infty \frac{n - 1}{n + 1}

f (x) = 7 x e^{x} csc (x)

x y^{^{'}} - 3 y = 7 x

What is the integral from-5 to 5 of pi(25-x^2) ?
The integral from-5 to 5 of pi(25-x^2) is pi 500/3