Aporte 1 - Regla del trapecio.docx - Aporte 1 2 Solucione...

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Aporte 1: 2. Solucione el siguiente ejercicio utilizando la Regla del Trapecio. (n= 4 ) 1 2 x 3 3 + x 1 / 2 dx Primero buscamos el valor de ∆ x (la fórmula es la siguiente). ∆ x = b a n Tenemos los valores: a= 1; b=2; n=4; Reemplazando estos valores en la formula tenemos. ∆ x = b a n = 2 1 4 = 1 4 ∆ x = 1 4 Ahora buscamos la x de manera sucesiva. x ¿ 0 = a = 1 x ¿ 1 = x ¿ 0 + ∆x = 1 + 1 4 = 5 4 = 1.25 x ¿ 2 = x ¿ 1 + ∆ x = 5 4 + 1 4 = 24 16 = 1.5 x ¿ 3 = x ¿ 2 + ∆x = 24 16 + 1 4 = 112 64 = 1.75 x ¿ 4 = x ¿ 3 + ∆ x = 112 64 + 1 4 = 512 256 = 2 Pasamos a sustituir dentro de nuestra función los valores de x f ( x 0 ) = X 3 3 + X 1 / 2 = ( 1 ) 3 3 +( 1 ) 1 / 2 = 0.25
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f ( x 1 ) = X 3 3 + X 1 / 2 = ( 1.25 ) 3 3 +( 1.25 ) 1 / 2 = 0.474286 f ( x 2 ) = X 3 3 + X 1 / 2 = ( 1.5 ) 3 3 +( 1.5 ) 1 / 2 = 0.798864 f ( x 3 ) = X 3 3 + X 1 / 2 = ( 1.75 ) 3 3 +( 1.75 ) 1 / 2 = 1.239770
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