What is the integral from 0 to 20 of 4(400-y^2) ?

The integral from 0 to 20 of 4(400-y^2) is 64000/3

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integral from 0 to 20 of 4(400-y^2)

\int_{0}^{20} 4 (400 - y^{2}) d y

\frac{64000}{3}

Decimal

21333.33333 \dots

Solution steps

\int_{0}^{20} 4 (400 - y^{2}) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{20} 400 - y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 (\int_{0}^{20} 400 d y - \int_{0}^{20} y^{2} d y)

\int_{0}^{20} 400 d y = 8000

\int_{0}^{20} y^{2} d y = \frac{8000}{3}

= 4 (8000 - \frac{8000}{3})

Simplify

4 (8000 - \frac{8000}{3}) : \frac{64000}{3}

= \frac{64000}{3}

What is the integral from 0 to 20 of 4(400-y^2) ?
The integral from 0 to 20 of 4(400-y^2) is 64000/3