What is the integral from 1 to x of xy ?

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

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integral from 1 to x of xy

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

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

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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