integral from 1 to 7 of 7/(sqrt(x-6))

解

\int_{1}^{7} \frac{7}{x - 6} d x

- 145 i + 14

解答ステップ

\int_{1}^{7} \frac{7}{x - 6} d x

未定義の (特異) 点を求める:

x = 6

存在する場合は

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

未定義

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

= \int_{1}^{6} \frac{7}{x - 6} d x + \int_{6}^{7} \frac{7}{x - 6} d x

\int_{1}^{6} \frac{7}{x - 6} d x = - 145 i

\int_{6}^{7} \frac{7}{x - 6} d x = 14

= - 145 i + 14