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

The integral from-1 to 1 of (1+2x-3x^2+x^3) is 0

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

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

0

Solution steps

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

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

\int_{- 1}^{1} 2 x d x = 0

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

\int_{- 1}^{1} x^{3} d x = 0

= 2 + 0 - 2 + 0

Simplify

= 0

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What is the integral from-1 to 1 of (1+2x-3x^2+x^3) ?
The integral from-1 to 1 of (1+2x-3x^2+x^3) is 0