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

The integral from-2 to 2 of (3x^2-x+1) is 20

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

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

20

Solution steps

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

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

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

\int_{- 2}^{2} 1 d x = 4

= 16 - 0 + 4

Simplify

= 20

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What is the integral from-2 to 2 of (3x^2-x+1) ?
The integral from-2 to 2 of (3x^2-x+1) is 20