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

解答

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

- 9

求解步骤

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

化简

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

使用积分加法定则:

\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

化简

= - 9

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