Your integral:
\(\displaystyle \L \int _{0}^\pi e^{cosx}sinx dx\)
\(\displaystyle u = cosx \\ du = -sinxdx \,\, \,\, \Rightarrow \,\,\,\, -du =sinxdx\)
So,
\(\displaystyle \L\int _{0}^\pi e^{cosx}sinx dx \,\, \,\, = \,\, \,\, \int _{1}^{-1} e^{u}(-du)\)
Which is the same as:
\(\displaystyle \L -\int _{1}^{-1} e^{u}(du) \,\, \,\, = \,\, \,\, \int _{-1}^{1} e^{u}(du)\)
Hope that helps,
-daon
