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

The integral from 0 to 1-x of x is ((-x+1)^2)/2

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integral from 0 to 1-x of x

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

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

Solution steps

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

Apply the Power Rule

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

Compute the boundaries:

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

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

Simplify

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

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