What is the integral from 0 to 1 of 12x^3 ?

The integral from 0 to 1 of 12x^3 is 3

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integral from 0 to 1 of 12x^3

\int_{0}^{1} 12 x^{3} d x

3

Solution steps

\int_{0}^{1} 12 x^{3} d x

Take the constant out:

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

= 12 \cdot \int_{0}^{1} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{1}

= 12 [\frac{x ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= 12 \cdot \frac{1}{4}

Simplify

= 3

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What is the integral from 0 to 1 of 12x^3 ?
The integral from 0 to 1 of 12x^3 is 3