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

The integral from-3 to 3 of (x^2+2x+3) is 36

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

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

36

Solution steps

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

\int_{- 3}^{3} x^{2} d x = 18

\int_{- 3}^{3} 2 x d x = 0

\int_{- 3}^{3} 3 d x = 18

= 18 + 0 + 18

Simplify

= 36

What is the integral from-3 to 3 of (x^2+2x+3) ?
The integral from-3 to 3 of (x^2+2x+3) is 36