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

The integral from-1 to 1 of (3x^2+x+1) is 4

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

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

4

Solution steps

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

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

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

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

= 2 + 0 + 2

Simplify

= 4

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What is the integral from-1 to 1 of (3x^2+x+1) ?
The integral from-1 to 1 of (3x^2+x+1) is 4