What is the integral from x to 1 of xy ?

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

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integral from x to 1 of xy

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

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

Solution steps

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

Take the constant out:

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

= x \cdot \int_{x}^{1} y d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2} - \frac{x ^{2}}{2}

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

Simplify

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

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