What is the integral from-2 to 2 of (x^5-x^3+3x^2-4) ?

The integral from-2 to 2 of (x^5-x^3+3x^2-4) is 0

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integral from-2 to 2 of (x^5-x^3+3x^2-4)

\int_{- 2}^{2} (x^{5} - x^{3} + 3 x^{2} - 4) d x

0

Solution steps

\int_{- 2}^{2} x^{5} - x^{3} + 3 x^{2} - 4 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_{- 2}^{2} x^{5} d x - \int_{- 2}^{2} x^{3} d x + \int_{- 2}^{2} 3 x^{2} d x - \int_{- 2}^{2} 4 d x

\int_{- 2}^{2} x^{5} d x = 0

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

\int_{- 2}^{2} 3 x^{2} d x = 16

\int_{- 2}^{2} 4 d x = 16

= 0 - 0 + 16 - 16

Simplify

= 0

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What is the integral from-2 to 2 of (x^5-x^3+3x^2-4) ?
The integral from-2 to 2 of (x^5-x^3+3x^2-4) is 0