integral from-pi to pi of e^{-inx}

解答

\int_{- π}^{π} e^{- in x} d x

0

求解步骤

\int_{- π}^{π} e^{- in x} d x

化简

e^{- in x} : cos (n x) - i sin (n x)

= \int_{- π}^{π} cos (n x) - i sin (n x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- π}^{π} cos (n x) d x - \int_{- π}^{π} i sin (n x) d x

\int_{- π}^{π} cos (n x) d x = 0

\int_{- π}^{π} i sin (n x) d x = 0

= 0 - 0

化简

= 0

d er i v a t i v e f (x) = \frac{4}{x}

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

x \to 0 lim (\frac{sin ( 3 x )}{x} + 2)

\frac{1}{x ^{4}} \frac{d y}{d x} = 19 + 15 y

\frac{d ^{2}}{d x ^{2}} (t^{3} (e)^{3 t})