What is the integral from 0 to 1 of 6(1-y) ?

The integral from 0 to 1 of 6(1-y) is 3

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integral from 0 to 1 of 6(1-y)

\int_{0}^{1} 6 (1 - y) d y

3

Solution steps

\int_{0}^{1} 6 (1 - y) d y

Take the constant out:

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

= 6 \cdot \int_{0}^{1} 1 - 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

= 6 (\int_{0}^{1} 1 d y - \int_{0}^{1} y d y)

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

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

= 6 (1 - \frac{1}{2})

Simplify

6 (1 - \frac{1}{2}) : 3

= 3

What is the integral from 0 to 1 of 6(1-y) ?
The integral from 0 to 1 of 6(1-y) is 3