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

解

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

- Si (- π) + Si (π)

解答ステップ

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

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

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

= - Si (- π) + Si (π)