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

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

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

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

\frac{4000}{3}

Decimal Notation

1333.33333 \dots

Solution steps

\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

= \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}

= 2000 - \frac{2000}{3}

Simplify

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

= \frac{4000}{3}

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