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

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

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

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

9

Solution steps

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

Expand

(2 x + 1) (2 x - 1) : 4 x^{2} - 1

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

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

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

= 12 - 3

Simplify

= 9

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