What is the integral from 0 to t of e^{-t+x}cos(x) ?

The integral from 0 to t of e^{-t+x}cos(x) is 1/2 sin(t)+1/2 cos(t)-1/2 e^{-t}

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integral from 0 to t of e^{-t+x}cos(x)

\int_{0}^{t} e^{- t + x} cos (x) d x

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

Solution steps

\int_{0}^{t} e^{- t + x} cos (x) d x

Compute the indefinite integral:

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

Compute the boundaries:

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

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

\int_{1}^{16} \frac{1}{1 + x} d x

\int_{2}^{\infty} u \cdot e^{- u} d u

\int_{- 2}^{1} x^{3} - 2 x^{2} - 5 x + 6 d x

\int_{0}^{1} e^{- x} cos (w x) d x

\int_{0}^{\frac{π}{2}} (e^{x} + cos (x)) d x

What is the integral from 0 to t of e^{-t+x}cos(x) ?
The integral from 0 to t of e^{-t+x}cos(x) is 1/2 sin(t)+1/2 cos(t)-1/2 e^{-t}