What is the integral from 0 to 40 of 400-x^2 ?

The integral from 0 to 40 of 400-x^2 is -16000/3

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integral from 0 to 40 of 400-x^2

\int_{0}^{40} 400 - x^{2} d x

- \frac{16000}{3}

Decimal

- 5333.33333 \dots

Solution steps

\int_{0}^{40} 400 - 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_{0}^{40} 400 d x - \int_{0}^{40} x^{2} d x

\int_{0}^{40} 400 d x = 16000

\int_{0}^{40} x^{2} d x = \frac{64000}{3}

= 16000 - \frac{64000}{3}

Simplify

16000 - \frac{64000}{3} : - \frac{16000}{3}

= - \frac{16000}{3}

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What is the integral from 0 to 40 of 400-x^2 ?
The integral from 0 to 40 of 400-x^2 is -16000/3