What is the integral from-2 to 2 of x^3+3x^2-2x+4 ?

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

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integral from-2 to 2 of x^3+3x^2-2x+4

\int_{- 2}^{2} x^{3} + 3 x^{2} - 2 x + 4 d x

32

Solution steps

\int_{- 2}^{2} x^{3} + 3 x^{2} - 2 x + 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^{3} d x + \int_{- 2}^{2} 3 x^{2} d x - \int_{- 2}^{2} 2 x d x + \int_{- 2}^{2} 4 d x

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

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

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

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

= 0 + 16 - 0 + 16

Simplify

= 32

\int_{2}^{6} (x + 1) (x^{2} + 2 x)^{2} d x

\int_{1}^{11} 1 d x

\int_{0}^{8} 8 y - y^{2} d y

\int_{- 4}^{0} x d x

\int_{- 2}^{1} (- 2 x + 4) d x

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