integral from-5 to 5 of (sin(x))/x

解

\int_{- 5}^{5} \frac{sin ( x )}{x} d x

- Si (- 5) + 1.54993 \dots

解答ステップ

\int_{- 5}^{5} \frac{sin ( x )}{x} d x

未定義の (特異) 点を求める:

x = 0

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_{- 5}^{0} \frac{sin ( x )}{x} d x + \int_{0}^{5} \frac{sin ( x )}{x} d x

\int_{- 5}^{0} \frac{sin ( x )}{x} d x = - Si (- 5)

\int_{0}^{5} \frac{sin ( x )}{x} d x = 1.54993 \dots

= - Si (- 5) + 1.54993 \dots