What is the integral from-2 to 1 of (-x^2-6x-9) ?

The integral from-2 to 1 of (-x^2-6x-9) is -21

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integral from-2 to 1 of (-x^2-6x-9)

\int_{- 2}^{1} (- x^{2} - 6 x - 9) d x

- 21

Solution steps

\int_{- 2}^{1} - x^{2} - 6 x - 9 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}^{1} x^{2} d x - \int_{- 2}^{1} 6 x d x - \int_{- 2}^{1} 9 d x

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

\int_{- 2}^{1} 6 x d x = - 9

\int_{- 2}^{1} 9 d x = 27

= - 3 - (- 9) - 27

Simplify

= - 21

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\int_{0}^{t} e^{2 x} d x

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

What is the integral from-2 to 1 of (-x^2-6x-9) ?
The integral from-2 to 1 of (-x^2-6x-9) is -21