integral from 0 to t of 5e^ssin(t-s)

解答

\int_{0}^{t} 5 e^{s} sin (t - s) d s

\frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

求解步骤

\int_{0}^{t} 5 e^{s} sin (t - s) d s

计算不定积分:

\int 5 e^{s} sin (t - s) d s = 5 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

带入上下限计算后得:

\int_{0}^{t} 5 e^{s} sin (t - s) d s = \frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

= \frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

\int \frac{cos ( x )}{( sin ^{2} ( x ) ) ^{\frac{1}{3}}} d x

x \to 0 lim (\frac{sin ( 14 x )}{x})

\int sin (e^{x}) d x

d er i v a t i v e f (x) = 8 (2 x - 3)^{3}

s l o p e in t erce pt (- 3, 7), (6, - 8)