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

The integral from-2 to 2 of 3/2 x^2 is 8

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

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

8

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{16}{3}

= \frac{3}{2} \cdot \frac{16}{3}

Simplify

= 8

x \to 1 lim (- x^{2} + 4 x)

x \to 2 + lim (\frac{x ^{2} - 2 x - 8}{x ^{2} - 5 x + 6})

\int \frac{x + 4}{x ^{2} + 8 x + 17} d x

\frac{d}{d x} (2 + \frac{1}{x})

f (x) = x (x + 1)^{2}

What is the integral from-2 to 2 of 3/2 x^2 ?
The integral from-2 to 2 of 3/2 x^2 is 8