∫ x 2 e -x ⁢ ⅆ x { F⁡(x)= x 2 g⁡(x)= e -x f⁡(x)=2x G⁡(x)=- e -x ⇒ ∫ x 2 e -x ⁢ ⅆ x =- x 2 e -x +2 ∫ x e -x ⁢ ⅆ x
∫ x e -x ⁢ ⅆ x { F⁡(x)=x g⁡(x)= e -x f⁡(x)=1 G⁡(x)=- e -x ⇒ ∫ x e -x ⁢ ⅆ x =-x e -x + ∫ e -x ⁢ ⅆ x =-x e x - e -x =- (x+1)· e -x

∫ x 2 e -x ⁢ ⅆ x =- x 2 e -x +2 ∫ x e -x ⁢ ⅆ x =- x 2 e -x -2( x+1 ) e -x =-( x 2 +2x+2 ) e -x 
∫ 1 3 x 2 e -x ⁢ ⅆ x = [ -( x 2 +2x+2 ) e -x ] 1 3 =-17 e -3 +5 e -1 ≃ 0.993017043606

Ampiezza del sottointervallo: ∆x= (b - a)/n= 2/10= 0.2
  • Metodo dei rettangoli

∫ 1 3 x 2 e -x ⁢ ⅆ x =0.2 ⋅ [ f⁡(1)+f(1.2)+f(1.4)+f(1.6)+f(1.8)+f(2.0)+f(2.2)+f(2.4)+f(2.6)+f(2.8) ]=


   =0.2 ⋅ [ (1 ) 2 e -1 +(1.2 ) 2 e -1.2 +(1.4 ) 2 e -1.4 +(1.6 ) 2 e -1.6 +(1.8 ) 2 e -1.8 +(2.0 ) 2 e -2.0 +(2.2 ) 2 e -2.2 +(2.4 ) 2 e -2.4 +(2.6 ) 2 e -2.6 +(2.8 ) 2 e -2.8 ]=0.9832713499


  • Metodo dei trapezi

∫ 1 3 x 2 e -x ⁢ ⅆ x =0.2 ⋅ [ f⁡(1)+f⁡(3) 2 +f(1.2)+f(1.4)+f(1.6)+f(1.8)+f(2.0)+f(2.2)+f(2.4)+f(2.6)+f(2.8) ]=
=0.2 ⋅ [ (1 ) 2 e -1 +(3 ) 2 e -3 2 +(1.2 ) 2 e -1.2 +(1.4 ) 2 e -1.4 +(1.6 ) 2 e -1.6 +(1.8 ) 2 e -1.8 +(2.0 ) 2 e -2.0 +(2.2 ) 2 e -2.2 +(2.4 ) 2 e -2.4 +(2.6 ) 2 e -2.6 +(2.8 ) 2 e -2.8 ]=0.9912917673


  • Metodo delle parabole
∫ 1 3 x 2 e -x ⁢ ⅆ x = 1 15 ⋅ { f⁡(1)+f⁡(3)+2 ⋅ [ f(1.4)+f(1.8)+f(2.2)+f(2.6) ]+4 ⋅ [ f(1.2)+f(1.6)+f(2.0)+f(2.4)+f(2.8) ] }=
= 1 15 ⋅ { (1 ) 2 e -1 +(3 ) 2 e -3 +2[ (1.4 ) 2 e -1.4 +(1.8 ) 2 e -1.8 +(2.2 ) 2 e -2.2 +(2.6 ) 2 e -2.6 ]+4 ⋅ [ (1.2 ) 2 e -1.2 +(1.6 ) 2 e -1.6 +(2.0 ) 2 e -2.0 +(2.4 ) 2 e -2.4 +(2.8 ) 2 e -2.8 ] }=0.9930214697