jueves, 26 de septiembre de 2019

suma integral

∫ [0 --> 1]-[f(x)] d[x]=( f(1/n)+...(n)...+f(n/n) )·m(n)
∫ [0 --> a]-[f(x)] d[x]=( f(a·(1/n))+...(n)...+f(a·(n/n)) )·( a·m(n) )


∫ [a --> b]-[f(x)] d[x]= ∫ [0 --> b]-[f(x)] d[x]+(-1)·∫ [0 --> a]-[f(x)] d[x]




∫ [0 --> 1]-[1] d[x]=( 1+...(n)...+1 )·(1/n)
∫ [0 --> 1]-[x] d[x]=( (1/n)+...(n)...+(n/n) )·(1/(n+1))


∫ [0 --> 1]-[x^{2}] d[x]=( (1/n)^{2}+...(n)...+(n/n)^{2} )·( 2n/((n+1)(2n+1)) )
∫ [0 --> 1]-[x^{3}] d[x]=( (1/n)^{3}+...(n)...+(n/n)^{3} )·( n/((n+1)(n+1)) )


∫ [0 --> 1]-[x^{4}] d[x]=( (1/n)^{4}+...(n)...+(n/n)^{4} )·( 2n·3n^{2}/((n+1)(2n+1)(3n^{2}+3n+(-1))) )
∫ [0 --> 1]-[x^{5}] d[x]=( (1/n)^{5}+...(n)...+(n/n)^{5} )·( n·2n^{2}/((n+1)(n+1)(2n^{2}+2n+(-1))) )




∫ [0 --> 1]-[e^{x}] d[x]=( e^{(0/n)}+e^{(1/n)}+...(n)...+e^{( (n+(-1))/n )} )·( e^{(1/n)}+(-1) )

No hay comentarios:

Publicar un comentario