integral de 0 a t de-10e^ssin(t-s)

Solución

\int_{0}^{t} - 10 e^{s} sin (t - s) d s

- 5 e^{t} + 10 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Pasos de solución

\int_{0}^{t} - 10 e^{s} sin (t - s) d s

Calcular la integral indefinida:

\int - 10 e^{s} sin (t - s) d s = - 10 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Calcular los limites:

\int_{0}^{t} - 10 e^{s} sin (t - s) d s = - 5 e^{t} - (- 10 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t)))

= - 5 e^{t} - (- 10 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t)))

Simplificar

= - 5 e^{t} + 10 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

\int \frac{1}{p ^{2} + 2 p} d p

\int_{0}^{1} (x + 4) (x - 5) d x

\frac{1.6}{3.2 s + 1}

\int \frac{4 x}{1 + 2 x} d x

x = y^{2}, x = y + 6