Question

Помогите , срочно !

π/6
∫ ^ecosx·sinx dx =
0

Answer 1

$intlimits_0^frac{pi}{6}e^{cosx}sinxdx\\int e^{cosx}sinxdxRightarrow left|begin{array}{ccc}cosx=t\-sinxdx=dt\sinxdx=-dtend{array}right|Rightarrow-int e^tdt=-e^t=-e^{cosx}\-----------------------------\\intlimits_0^frac{pi}{6}e^{cosx}sinxdx=left-e^{cosx}right]^frac{pi}{6}_0=-e^{cosfrac{pi}{6}}-left(-e^{cos0}right)=-e^frac{sqrt3}{2}+e^1\=e-e^frac{sqrt3}{2}$

Answer 2

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