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

The integral from y-1 to 1-y of x is 0

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integral from y-1 to 1-y of x

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

0

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

= 0

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