What is the integral from-c to c of 3/2 x^2 ?

The integral from-c to c of 3/2 x^2 is c^3

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integral from-c to c of 3/2 x^2

\int_{- c}^{c} \frac{3}{2} x^{2} d x

c^{3}

Solution steps

\int_{- c}^{c} \frac{3}{2} x^{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_{- c}^{c} x^{2} d x

Apply the Power Rule

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

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

Compute the boundaries:

2 \cdot \frac{c ^{3}}{3}

= \frac{3}{2} \cdot 2 \cdot \frac{c ^{3}}{3}

Simplify

= c^{3}

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What is the integral from-c to c of 3/2 x^2 ?
The integral from-c to c of 3/2 x^2 is c^3