What is the integral from 0 to 1 of 100(4-sqrt(4y)) ?

The integral from 0 to 1 of 100(4-sqrt(4y)) is 800/3

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integral from 0 to 1 of 100(4-sqrt(4y))

\int_{0}^{1} 100 (4 - 4 y) d y

\frac{800}{3}

Decimal

266.66666 \dots

Solution steps

\int_{0}^{1} 100 (4 - 4 y) d y

Take the constant out:

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

= 100 \cdot \int_{0}^{1} 4 - 4 y d y

4 y = 2 y

= 100 \cdot \int_{0}^{1} 4 - 2 y 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

= 100 (\int_{0}^{1} 4 d y - \int_{0}^{1} 2 y d y)

\int_{0}^{1} 4 d y = 4

\int_{0}^{1} 2 y d y = \frac{4}{3}

= 100 (4 - \frac{4}{3})

Simplify

100 (4 - \frac{4}{3}) : \frac{800}{3}

= \frac{800}{3}

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What is the integral from 0 to 1 of 100(4-sqrt(4y)) ?
The integral from 0 to 1 of 100(4-sqrt(4y)) is 800/3