What is the integral from 0 to 1-x of 24xy ?

The integral from 0 to 1-x of 24xy is 12x(-x+1)^2

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integral from 0 to 1-x of 24xy

\int_{0}^{1 - x} 24 x y d y

12 x (- x + 1)^{2}

Solution steps

\int_{0}^{1 - x} 24 x y d y

Take the constant out:

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

= 24 x \cdot \int_{0}^{1 - x} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{1 - x}

= 24 x [\frac{y ^{2}}{2}]_{0}^{1 - x}

Compute the boundaries:

\frac{( - x + 1 ) ^{2}}{2}

= 24 x \frac{( - x + 1 ) ^{2}}{2}

Simplify

= 12 x (- x + 1)^{2}

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What is the integral from 0 to 1-x of 24xy ?
The integral from 0 to 1-x of 24xy is 12x(-x+1)^2