integral from-3 to 3 of (2-x)^5

解答

\int_{- 3}^{3} (2 - x)^{5} d x

2604

求解步骤

\int_{- 3}^{3} (2 - x)^{5} d x

乘以

2 - x

的共轭根式

: \frac{4 - x ^{2}}{2 + x}

= \int_{- 3}^{3} (\frac{4 - x ^{2}}{2 + x})^{5} d x

找到无定义的点（奇点）:

x = - 2

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 3}^{- 2} (\frac{4 - x ^{2}}{2 + x})^{5} d x + \int_{- 2}^{3} (\frac{4 - x ^{2}}{2 + x})^{5} d x

\int_{- 3}^{- 2} (\frac{4 - x ^{2}}{2 + x})^{5} d x = \frac{3843}{2}

\int_{- 2}^{3} (\frac{4 - x ^{2}}{2 + x})^{5} d x = \frac{1365}{2}

= \frac{3843}{2} + \frac{1365}{2}

化简

\frac{3843}{2} + \frac{1365}{2} : 2604

= 2604

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