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

The integral from-2 to 2 of (x^3-2x+3) is 12

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integral from-2 to 2 of (x^3-2x+3)

\int_{- 2}^{2} (x^{3} - 2 x + 3) d x

12

Solution steps

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

\int_{- 2}^{2} x^{3} d x = 0

\int_{- 2}^{2} 2 x d x = 0

\int_{- 2}^{2} 3 d x = 12

= 0 - 0 + 12

Simplify

= 12

\int (6 x^{2} y - 2 x) d y

\int_{0}^{1} - 9 (x^{2} + 1) e^{- x} d x

y = (1 + 2 x)^{2}, (1, 9)

\frac{\partial}{\partial x} (arctan (y x))

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

What is the integral from-2 to 2 of (x^3-2x+3) ?
The integral from-2 to 2 of (x^3-2x+3) is 12