integral from 0 to 3 of x/(sqrt(7-x^2))

解答

\int_{0}^{3} \frac{x}{7 - x ^{2}} d x

7 - 2 i

求解步骤

\int_{0}^{3} \frac{x}{7 - x ^{2}} d x

根据未定义的点调整积分在积分范围内有个未定义的点

: 7

= \int_{0}^{7} \frac{x}{7 - x ^{2}} d x + \int_{7}^{3} \frac{x}{7 - x ^{2}} d x

\int_{0}^{7} \frac{x}{7 - x ^{2}} d x = 7

= 7 + \int_{7}^{3} \frac{x}{7 - x ^{2}} d x

\int_{7}^{3} \frac{x}{7 - x ^{2}} d x = - 2 i

= 7 - 2 i

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