What is the integral from 0 to 3 of 1/3 x^2 ?

The integral from 0 to 3 of 1/3 x^2 is 3

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integral from 0 to 3 of 1/3 x^2

\int_{0}^{3} \frac{1}{3} x^{2} d x

3

Solution steps

\int_{0}^{3} \frac{1}{3} x^{2} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{3} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{3}

= \frac{1}{3} [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= \frac{1}{3} \cdot 9

Simplify

= 3

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What is the integral from 0 to 3 of 1/3 x^2 ?
The integral from 0 to 3 of 1/3 x^2 is 3