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

The integral from 2 to-2 of x^2-4 is 32/3

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integral from 2 to-2 of x^2-4

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

\frac{32}{3}

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (\int_{- 2}^{2} x^{2} d x - \int_{- 2}^{2} 4 d x)

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 4 d x = 16

= - (\frac{16}{3} - 16)

Simplify

- (\frac{16}{3} - 16) : \frac{32}{3}

= \frac{32}{3}

\int_{- 1}^{0} - x^{3} d x

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\int_{- 2}^{2} (11 - ∣ x ∣^{3}) d x

\int_{0}^{1} (- 1 - x^{2}) d x

What is the integral from 2 to-2 of x^2-4 ?
The integral from 2 to-2 of x^2-4 is 32/3