Riemann sums are a fundamental tool in calculus used to approximate the area under a curve by dividing the region into various geometric shapes, typically rectangles . As the number of these rectangles (

Calcular ( \Delta x ): [ \Delta x = \frac2 - 04 = 0.5 ]

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• (a=0,\ b=2,\ n=5,\ \Delta x=0.4)
• (x_i = 0, 0.4, 0.8, 1.2, 1.6, 2.0)
• Right sum = (0.4[f(0.4)+f(0.8)+f(1.2)+f(1.6)+f(2.0)])
• (f(0.4)=e^0.4\approx 1.49182)
• (f(0.8)\approx 2.22554)
• (f(1.2)\approx 3.32012)
• (f(1.6)\approx 4.95303)
• (f(2.0)=7.38906)
• Sum = (19.37957)
• Right sum ≈ (0.4 \times 19.37957 = 7.75183)

For a partition (a = x_0 < x_1 < \dots < x_n = b):

Para dominar este tema, la práctica es fundamental. Hemos preparado un documento que incluye: Sumas por izquierda, derecha y punto medio. Uso de fórmulas de sumatorias de potencias ( Cálculo de áreas exactas mediante límites.