What is the integral from 3 to 4 of 3x^2 ?

The integral from 3 to 4 of 3x^2 is 37

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integral from 3 to 4 of 3x^2

\int_{3}^{4} 3 x^{2} d x

37

Solution steps

\int_{3}^{4} 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int_{3}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{3}^{4}

= 3 [\frac{x ^{3}}{3}]_{3}^{4}

Compute the boundaries:

\frac{37}{3}

= 3 \cdot \frac{37}{3}

Simplify

= 37

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What is the integral from 3 to 4 of 3x^2 ?
The integral from 3 to 4 of 3x^2 is 37