integral from 0 to t of 9e^ssin(t-s)

Lösung

\int_{0}^{t} 9 e^{s} sin (t - s) d s

\frac{9}{2} e^{t} - 9 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Schritte zur Lösung

\int_{0}^{t} 9 e^{s} sin (t - s) d s

Berechne das unbestimmte Integral:

\int 9 e^{s} sin (t - s) d s = 9 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Berechne die Grenzen:

\int_{0}^{t} 9 e^{s} sin (t - s) d s = \frac{9}{2} e^{t} - 9 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

= \frac{9}{2} e^{t} - 9 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

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

x \to 0 + lim (2)

l a pl a ce t r an s f or m t

x \to \infty lim (- (x^{2}))

\frac{d}{d x} (\frac{2 ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{2}})