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

The integral from-1 to x of 3/2 x^2 is (x^3+1)/2

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integral from-1 to x of 3/2 x^2

\int_{- 1}^{x} \frac{3}{2} x^{2} d x

\frac{x ^{3} + 1}{2}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{3}}{3} + \frac{1}{3}

= \frac{3}{2} (\frac{x ^{3}}{3} + \frac{1}{3})

Simplify

= \frac{x ^{3} + 1}{2}

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What is the integral from-1 to x of 3/2 x^2 ?
The integral from-1 to x of 3/2 x^2 is (x^3+1)/2