Sumas De Riemann Ejercicios Resueltos Pdf May 2026

: [ R_4 = 0.5 [f(0.5) + f(1) + f(1.5) + f(2)] = 0.5 [0.25 + 1 + 2.25 + 4] = 0.5 \times 7.5 = 3.75 ]

[ \int_a^b f(x) , dx = \lim_n \to \infty \sum_i=1^n f(x_i^*) \Delta x ] sumas de riemann ejercicios resueltos pdf

Sum: (\sum_i=0^n-1 4 = 4n,\ \sum_i=0^n-1 \frac6in = \frac6n \cdot \fracn(n-1)2 = 3(n-1)) : [ R_4 = 0

Exact: (\int_1^3 (3x+1)dx = \left[\frac3x^22 + x\right]_1^3 = \left(\frac272+3\right) - \left(\frac32+1\right) = (13.5+3)-(1.5+1)=16.5-2.5=14) \ \sin(7\pi/8) = \sin(\pi/8)) Similarly

Note: (\sin(5\pi/8) = \sin(3\pi/8),\ \sin(7\pi/8) = \sin(\pi/8))

Similarly, (R_n = 14 + \frac6n) (check: (R_n = L_n + \Delta x (f(b)-f(a)))? (f(b)-f(a)=6,\ \Delta x \cdot 6 = \frac12n), but careful – compute:)