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Beliebt Rechnen >

integral from 0 to t of 3e^ssin(t-s)

Lösung

\int_{0}^{t} 3 e^{s} sin (t - s) d s

Lösung

\frac{3}{2} e^{t} - 3 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Schritte zur Lösung

\int_{0}^{t} 3 e^{s} sin (t - s) d s

Berechne das unbestimmte Integral:

\int 3 e^{s} sin (t - s) d s = 3 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Berechne die Grenzen:

\int_{0}^{t} 3 e^{s} sin (t - s) d s = \frac{3}{2} e^{t} - 3 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

= \frac{3}{2} e^{t} - 3 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Beliebte Beispiele

integral of 1/(2x+3)

\int \frac{1}{2 x + 3} d x

integral of (cos(x)sin(x))

\int (cos (x) sin (x)) d x

limit as x approaches 0 of (2x)/(|x|)

x \to 0 lim (\frac{2 x}{∣ x ∣})

(dy)/(dx)=(3xsqrt(y))

\frac{d y}{d x} = (3 x y)

integral of 4x-x^3

\int 4 x - x^{3} d x