La suma de Riemann se define como: $$S_n = \sum_i=1^n f(x_i^*) \Delta x$$

At its core, a is a method for approximating the total area under a curve on a graph. Before we had the Fundamental Theorem of Calculus to solve integrals instantly, mathematicians used this method of "exhaustion"—filling the space under a curve with rectangles.

sum from i equals 1 to n of f of open paren x sub i raised to the * power close paren delta x : The width of each sub-interval. x sub i raised to the * power : The sample point within the -th sub-interval. Departamento de Matemáticas | Uniandes Solved Example: Area under Find the area under on the interval using a right Riemann sum with sub-intervals. Departamento de Matemáticas | Uniandes 1. Calculate the sub-interval width Using the formula

La clave para dominar este tema es la práctica constante con ejercicios variados. Un debe incluir:

| Tipo de suma | Fórmula | Cuándo se usa | | :--- | :--- | :--- | | | ( \sum_i=0^n-1 f(a + i\Delta x) \Delta x ) | Subestima si ( f ) creciente | | Extremo derecho | ( \sum_i=1^n f(a + i\Delta x) \Delta x ) | Subestima si ( f ) decreciente | | Punto medio | ( \sum_i=1^n f\left(a + (i-0.5)\Delta x\right) \Delta x ) | Más preciso (error más pequeño) | | Trapecios | ( \frac\Delta x2 \sum_i=1^n [f(x_i-1) + f(x_i)] ) | Promedia izquierda + derecha |