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

The integral from-1 to 2 of (3x^2-2x+3) is 15

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

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

15

Solution steps

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

\int_{- 1}^{2} 3 x^{2} d x = 9

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

\int_{- 1}^{2} 3 d x = 9

= 9 - 3 + 9

Simplify

= 15

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What is the integral from-1 to 2 of (3x^2-2x+3) ?
The integral from-1 to 2 of (3x^2-2x+3) is 15