Помогите , срочно ! π/6 ∫ ^ecosx·sinx dx = 0

[latex]\int\limits_0^\frac{\pi}{6}e^{cosx}sinxdx\\\\\int e^{cosx}sinxdx\Rightarrow \left|\begin{array}{ccc}cosx=t\\-sinxdx=dt\\sinxdx=-dt\end{array}\right|\Rightarrow-\int e^tdt=-e^t=-e^{cosx}\\-----------------------------\\\\\int\limits_0^\frac{\pi}{6}e^{cosx}sinxdx=\left-e^{cosx}\right]^\frac{\pi}{6}_0=-e^{cos\frac{\pi}{6}}-\left(-e^{cos0}\right)=-e^\frac{\sqrt3}{2}+e^1\\=e-e^\frac{\sqrt3}{2}[/latex]

u=e^cosx⇒du=-sinx*e^cosxdx S(от 0 до π/6)(e^cosx*sinxdx=-S(от 0 до π/6)du=-u=-e^cosx(от 0 до π/6)= =-e^cosπ/6+e^cos0=-e^√3/2+e