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

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

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

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

9

Solution steps

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

Simplify

= \int_{- 2}^{1} 2 y^{2} + 1 d y

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 y^{2} d y + \int_{- 2}^{1} 1 d y

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

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

= 6 + 3

Simplify

= 9

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