What is the integral from-3 to 3 of (3x^3-2x^2+x+1) ?

The integral from-3 to 3 of (3x^3-2x^2+x+1) is -30

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integral from-3 to 3 of (3x^3-2x^2+x+1)

\int_{- 3}^{3} (3 x^{3} - 2 x^{2} + x + 1) d x

- 30

Solution steps

\int_{- 3}^{3} 3 x^{3} - 2 x^{2} + x + 1 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} 3 x^{3} d x - \int_{- 3}^{3} 2 x^{2} d x + \int_{- 3}^{3} x d x + \int_{- 3}^{3} 1 d x

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

\int_{- 3}^{3} 2 x^{2} d x = 36

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

\int_{- 3}^{3} 1 d x = 6

= 0 - 36 + 0 + 6

Simplify

= - 30

What is the integral from-3 to 3 of (3x^3-2x^2+x+1) ?
The integral from-3 to 3 of (3x^3-2x^2+x+1) is -30