What is the integral of (-x^2)/4 ?

The integral of (-x^2)/4 is -(x^3)/(12)+C

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integral of (-x^2)/4

\int \frac{- x ^{2}}{4} d x

- \frac{x ^{3}}{12} + C

Solution steps

\int \frac{- x ^{2}}{4} d x

Take the constant out:

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

= \frac{- 1}{4} \cdot \int x^{2} d x

Simplify

= (- \frac{1}{4}) \cdot \int x^{2} d x

Apply the Power Rule

= (- \frac{1}{4}) \frac{x ^{3}}{3}

Simplify

(- \frac{1}{4}) \frac{x ^{3}}{3} : - \frac{x ^{3}}{12}

= - \frac{x ^{3}}{12}

Add a constant to the solution

= - \frac{x ^{3}}{12} + C