What is the integral from-1 to 1 of (6x^2-2x+1) ?

The integral from-1 to 1 of (6x^2-2x+1) is 6

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integral from-1 to 1 of (6x^2-2x+1)

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

6

Solution steps

\int_{- 1}^{1} 6 x^{2} - 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_{- 1}^{1} 6 x^{2} d x - \int_{- 1}^{1} 2 x d x + \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} 6 x^{2} d x = 4

\int_{- 1}^{1} 2 x d x = 0

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

= 4 - 0 + 2

Simplify

= 6

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What is the integral from-1 to 1 of (6x^2-2x+1) ?
The integral from-1 to 1 of (6x^2-2x+1) is 6