By working through the , you ensure that you understand the "why" behind the integral symbol $\int$. This conceptual clarity is crucial for more advanced topics like numerical analysis and differential equations.
S3=[f(x1)+f(x2)+f(x3)]⋅Δxcap S sub 3 equals open bracket f of open paren x sub 1 close paren plus f of open paren x sub 2 close paren plus f of open paren x sub 3 close paren close bracket center dot delta x
sum from i equals 1 to n of f of open paren x sub i close paren delta x equals sum from i equals 1 to n of open paren the fraction with numerator 4 i squared and denominator n squared end-fraction close paren open paren 2 over n end-fraction close paren equals sum from i equals 1 to n of the fraction with numerator 8 i squared and denominator n cubed end-fraction 3. Simplificar con sumas notables Extraemos las constantes y aplicamos la fórmula para
Calcule la suma de Riemann por el punto medio para la función f(x) = 3x en el intervalo [1, 3] con 6 subintervalos.
[ \int_0^2 (x^2 + 6x + 9) , dx = \left[ \fracx^33 + 3x^2 + 9x \right]_0^2 ] [ = \left( \frac83 + 12 + 18 \right) - 0 = \frac83 + 30 = \frac8 + 903 = \frac983 \approx 32.666 ]
Dependiendo del extremo del rectángulo que toques para medir la altura, la fórmula cambia: Por la izquierda: 3. La Suma de Riemann (Por la derecha)
