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

The integral from 0 to 3 of (3x^2)/2 is 27/2

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integral from 0 to 3 of (3x^2)/2

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

\frac{27}{2}

Decimal

13.5

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{3}{2} [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= \frac{3}{2} \cdot 9

Simplify

= \frac{27}{2}

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What is the integral from 0 to 3 of (3x^2)/2 ?
The integral from 0 to 3 of (3x^2)/2 is 27/2