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

The integral from-1 to 3 of (x^3-3x^2-1) is -12

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

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

- 12

Solution steps

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

\int_{- 1}^{3} x^{3} d x = 20

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 1 d x = 4

= 20 - 28 - 4

Simplify

= - 12

What is the integral from-1 to 3 of (x^3-3x^2-1) ?
The integral from-1 to 3 of (x^3-3x^2-1) is -12