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

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

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

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

- 2

Solution steps

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

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

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

= 0 - 2

Simplify

= - 2

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\int_{0}^{2} 11 x (x^{2} + 1)^{2} d x

\int_{1}^{2} (2 x^{3} - 1)^{2} 6 x^{2} d x

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