Calcula a integral definida ∫01x⋅ex dx\int_0^1 x \cdot e^{x} \, dx∫01x⋅exdx.
By parts: ∫x⋅ex dx=ex(x−1)\int x \cdot e^{x} \, dx = e^{x}(x-1)∫x⋅exdx=ex(x−1). Evaluate: [ex(x−1)]01=e(0)−e0(−1)=0+1=1[e^{x}(x-1)]_0^1 = e(0) - e^{0}(-1) = 0 + 1 = 1[ex(x−1)]01=e(0)−e0(−1)=0+1=1