Matematica
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Ejercicio Determine el área de la región acotada por la curva de y = 2x, el eje x, y las rectas x = 0 y x = 4. Use rectángulos circunscritos.
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![𝒜 = 𝐵 . 𝐻
𝐴𝑡= 𝐴1+ 𝐴2+ 𝐴3+ 𝐴4
𝐴𝑡= 1𝑓(1) + 1𝑓(2) + 1𝑓(3) + 1𝑓(4)
𝐴𝑡= 1[𝑓(1) + 𝑓(2) + 𝑓(3) + 𝑓(4)]
∑ 𝑓(𝑖)
𝑛
𝑖=1
∑ 𝑖 =
𝑛(𝑛 + 1)
2
𝑛
𝑖=1
∑ 2𝑖 = 2 ∑ 𝑖
4
𝑖=1
4
𝑖=1
𝐴 = 2 ∑
𝑛(𝑛 + 1)
2
4
𝑖=1
𝐴 =
2 .4(4+1)
2
≈20](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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- 2. 𝒜 = 𝐵 . 𝐻 𝐴𝑡= 𝐴1+ 𝐴2+ 𝐴3+ 𝐴4 𝐴𝑡= 1𝑓(1) + 1𝑓(2) + 1𝑓(3) + 1𝑓(4) 𝐴𝑡= 1[𝑓(1) + 𝑓(2) + 𝑓(3) + 𝑓(4)] ∑ 𝑓(𝑖) 𝑛 𝑖=1 ∑ 𝑖 = 𝑛(𝑛 + 1) 2 𝑛 𝑖=1 ∑ 2𝑖 = 2 ∑ 𝑖 4 𝑖=1 4 𝑖=1 𝐴 = 2 ∑ 𝑛(𝑛 + 1) 2 4 𝑖=1 𝐴 = 2 .4(4+1) 2 ≈20