What is the integral from-1 to 2 of (x^2+4x+6) ?

The integral from-1 to 2 of (x^2+4x+6) is 27

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integral from-1 to 2 of (x^2+4x+6)

\int_{- 1}^{2} (x^{2} + 4 x + 6) d x

27

Solution steps

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

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

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

\int_{- 1}^{2} 6 d x = 18

= 3 + 6 + 18

Simplify

= 27

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What is the integral from-1 to 2 of (x^2+4x+6) ?
The integral from-1 to 2 of (x^2+4x+6) is 27