What is the integral from-10 to 10 of pi(100-x^2) ?

The integral from-10 to 10 of pi(100-x^2) is pi 4000/3

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integral from-10 to 10 of pi(100-x^2)

\int_{- 10}^{10} π (100 - x^{2}) d x

π \frac{4000}{3}

Decimal

4188.79020 \dots

Solution steps

\int_{- 10}^{10} π (100 - 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_{- 10}^{10} 100 - 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_{- 10}^{10} 100 d x - \int_{- 10}^{10} x^{2} d x)

\int_{- 10}^{10} 100 d x = 2000

\int_{- 10}^{10} x^{2} d x = \frac{2000}{3}

= π (2000 - \frac{2000}{3})

Join

2000 - \frac{2000}{3} : \frac{4000}{3}

= π \frac{4000}{3}

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What is the integral from-10 to 10 of pi(100-x^2) ?
The integral from-10 to 10 of pi(100-x^2) is pi 4000/3