What is the integral from-2 to 4 of (x^2)/2 ?

The integral from-2 to 4 of (x^2)/2 is 12

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integral from-2 to 4 of (x^2)/2

\int_{- 2}^{4} \frac{x ^{2}}{2} d x

12

Solution steps

\int_{- 2}^{4} \frac{x ^{2}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{- 2}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 2}^{4}

= \frac{1}{2} [\frac{x ^{3}}{3}]_{- 2}^{4}

Compute the boundaries:

24

= \frac{1}{2} \cdot 24

Simplify

= 12

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What is the integral from-2 to 4 of (x^2)/2 ?
The integral from-2 to 4 of (x^2)/2 is 12