What is the integral from-1 to 2 of (-2x^2+2x+4) ?

The integral from-1 to 2 of (-2x^2+2x+4) is 9

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integral from-1 to 2 of (-2x^2+2x+4)

\int_{- 1}^{2} (- 2 x^{2} + 2 x + 4) d x

9

Solution steps

\int_{- 1}^{2} - 2 x^{2} + 2 x + 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_{- 1}^{2} 2 x^{2} d x + \int_{- 1}^{2} 2 x d x + \int_{- 1}^{2} 4 d x

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

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

\int_{- 1}^{2} 4 d x = 12

= - 6 + 3 + 12

Simplify

= 9

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\int_{0}^{2} (- 2 x^{2} + 4 x) d x

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

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

What is the integral from-1 to 2 of (-2x^2+2x+4) ?
The integral from-1 to 2 of (-2x^2+2x+4) is 9