What is the integral from 0 to t of 7e^ssin(t-s) ?

The integral from 0 to t of 7e^ssin(t-s) is 7/2 e^t-7(1/2 cos(t)+1/2 sin(t))

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integral from 0 to t of 7e^ssin(t-s)

\int_{0}^{t} 7 e^{s} sin (t - s) d s

\frac{7}{2} e^{t} - 7 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Solution steps

\int_{0}^{t} 7 e^{s} sin (t - s) d s

Compute the indefinite integral:

\int 7 e^{s} sin (t - s) d s = 7 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Compute the boundaries:

\int_{0}^{t} 7 e^{s} sin (t - s) d s = \frac{7}{2} e^{t} - 7 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

= \frac{7}{2} e^{t} - 7 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

\frac{d y}{d x} = \frac{2 sec ( y )}{( x - 4 ) ^{2}}

\int x^{4} e^{x^{5 + 2}} d x

e^{x}, e^{- 3 x}, ln (6)

\frac{d}{d x} (\frac{x}{3 a} (a - x))

\int 4 e^{- 0.5 x} d x

What is the integral from 0 to t of 7e^ssin(t-s) ?
The integral from 0 to t of 7e^ssin(t-s) is 7/2 e^t-7(1/2 cos(t)+1/2 sin(t))