What is the integral of (x^2)/(12) ?

The integral of (x^2)/(12) is (x^3)/(36)+C

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integral of (x^2)/(12)

\int \frac{x ^{2}}{12} d x

\frac{x ^{3}}{36} + C

Solution steps

\int \frac{x ^{2}}{12} d x

Take the constant out:

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

= \frac{1}{12} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{12} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{12} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{36}

= \frac{x ^{3}}{36}

Add a constant to the solution

= \frac{x ^{3}}{36} + C

f (x) = 8 6 x^{2} + 7

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