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

The integral from-3 to 3 of x^3+3x^2+2x is 54

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

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

54

Solution steps

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

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

\int_{- 3}^{3} 3 x^{2} d x = 54

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

= 0 + 54 + 0

Simplify

= 54

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What is the integral from-3 to 3 of x^3+3x^2+2x ?
The integral from-3 to 3 of x^3+3x^2+2x is 54