What is the integral from-1 to 3 of (3x^2-x+6) ?

The integral from-1 to 3 of (3x^2-x+6) is 48

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integral from-1 to 3 of (3x^2-x+6)

\int_{- 1}^{3} (3 x^{2} - x + 6) d x

48

Solution steps

\int_{- 1}^{3} 3 x^{2} - x + 6 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}^{3} 3 x^{2} d x - \int_{- 1}^{3} x d x + \int_{- 1}^{3} 6 d x

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} x d x = 4

\int_{- 1}^{3} 6 d x = 24

= 28 - 4 + 24

Simplify

= 48

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What is the integral from-1 to 3 of (3x^2-x+6) ?
The integral from-1 to 3 of (3x^2-x+6) is 48