What is the integral from 1 to 3 of 12x^2 ?

The integral from 1 to 3 of 12x^2 is 104

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integral from 1 to 3 of 12x^2

\int_{1}^{3} 12 x^{2} d x

104

Solution steps

\int_{1}^{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_{1}^{3} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{3}

= 12 [\frac{x ^{3}}{3}]_{1}^{3}

Compute the boundaries:

\frac{26}{3}

= 12 \cdot \frac{26}{3}

Simplify

= 104

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What is the integral from 1 to 3 of 12x^2 ?
The integral from 1 to 3 of 12x^2 is 104