Calculo Integral

By leidy.tatis2310 | Updated: Oct. 7, 2024, 3:36 p.m.

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Los Inge INSO 
Jessica Chala
William Parada 
Tatiana Peña
Calculo Integral
Hallar el área de la región limitada por la gráfica de f(x)=2𝑥2 − 2 en el intervalo
[-1,3], cuando n= 4. Mediante el cálculo de las sumas de Riemann
F(X)=〖2X〗^2-2           [-1,3]            n=4

Hallar Δ Delta            ΔX=  (b-a)/n

ΔX=  (3-(-1))/4 = 4/4  = 1

Vanessa - HR
XI = Por la Derecha:  a+ ΔX*і
XI = Por la Izquierda:  a +( і-1) ΔX

XI PD =  -1 + 1*і               
 XI  PI = -1 +( і-1) 1

XI =  [-1+1*i +(-1+(i-1)1) ]
XI =  [-1+1*i +(-1+(i-1)]
XI =  [-1+1*i -1+i-1]
XI =  -3+2i

F(X)=〖2X〗^2-2           
lim┬(n→∞)  ∑ [(〖2(-3+2i)〗^2  – 2) ] *1
lim┬(n→∞)   ∑ [(〖2(9+2(-6i)+(2i)〗^2  – 2) ] *1
∑ [(〖2(9i 2i+4i〗^2) -2] *1
∑ [(18i 24i+8i^2-2 ] *1
∑ [(16i 24i+8i^2] *1
16i 24i+8i^2

∑16 + ∑-24i +∑8^2
  16*4 -24i ∑i=10 + 8∑i^2=30
64-240+240
64u^2

Hallar el área de la región limitada por la gráfica de f(x)=𝑥 − 1 en el intervalo
[0,2], cuando n= 6. Mediante el cálculo de las sumas de Riemann
F(X)= X -1            [0,2]            n=6

Hallar Δ Delta         
ΔX=  (b-a)/n

ΔX=  (2-0)/6 = 2/6  = 1/3

XI = Por la Derecha:  a+ ΔX*і
XI = Por la Izquierda:  a +( і-1) ΔX

XI PD =  0 + 1/3*і                                                  
XI  PI = 0 +( і-1) 1/3

XI =  [1/3*i +((i-1) 1/3) ]
XI =  [1/3*i +i 1/3 -  1/3]
XI =  [2/3*i -  1/3]

F(X)=X- 1           
lim┬(n→∞)  ∑ [(2/3  i– 1/3)-1 ] *1/3
lim┬(n→∞)  ∑ [(2/3  i– 4/3) ] *1/3
lim┬(n→∞)  ∑ [(2/9  i– 4/9) ]
  ∑2/9 * ∑ i=21 +∑4/( 9)*6
14/3-  8/3 = 〖2u〗^2

GRACIAS...
Calculo Integral
11/09/2024
Los inge INSO

Calculo Integral

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