What is the integral of (y-x)^2 ?

The integral of (y-x)^2 is -((y-x)^3)/3+C

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integral of (y-x)^2

\int (y - x)^{2} d x

- \frac{( y - x ) ^{3}}{3} + C

Solution steps

\int (y - x)^{2} d x

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

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

= - \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= - \frac{u ^{3}}{3}

Substitute back

u = y - x

= - \frac{( y - x ) ^{3}}{3}

Add a constant to the solution

= - \frac{( y - x ) ^{3}}{3} + C

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