What is the integral from 0 to 3 of 12x^2 ?

The integral from 0 to 3 of 12x^2 is 108

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integral from 0 to 3 of 12x^2

\int_{0}^{3} 12 x^{2} d x

108

Solution steps

\int_{0}^{3} 12 x^{2} d x

Take the constant out:

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

= 12 \cdot \int_{0}^{3} x^{2} d x

Apply the Power Rule

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

= 12 [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= 12 \cdot 9

Simplify

= 108

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\int_{0}^{3} (x 1 + x) d x

\int_{0}^{r} b \cdot r^{3} + c \cdot r^{2} d r

What is the integral from 0 to 3 of 12x^2 ?
The integral from 0 to 3 of 12x^2 is 108