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

The integral from-2 to 1 of (3+x^2)-(2-x^2) is 9

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

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

9

Solution steps

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

Simplify

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

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

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

= 6 + 3

Simplify

= 9

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What is the integral from-2 to 1 of (3+x^2)-(2-x^2) ?
The integral from-2 to 1 of (3+x^2)-(2-x^2) is 9