1. Let f(x) = 3x-x² be defined on [0,2]. Find the right Riemann sum relative to the regular partitions P₂, P3, P4. From this these three approximations, could you guess what is the area of the region bounded by y = 3x-x² and the x-axis on [0,2]?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Answer the following problems.
Answer the following questions:
1. Let f(x) = 3x-x² be defined on [0,2]. Find the right Riemann sum relative to the regular partitions P2, P3, P4. From this
these three approximations, could you guess what is the area of the region bounded by y = 3x - x² and the x-axis on
[0,2]?
2.
Let f(x) = be defined on [0,1]. Find the left, right, and midpoint Riemann sums relative to the regular partitions
P₂ and P3.
x+1
3.
Let f(x) =tan tan x defined on [0, π/4]. Find the left, right, and midpoint Riemann sums relative to the regular
partitions P₂ and P3.
Transcribed Image Text:Answer the following questions: 1. Let f(x) = 3x-x² be defined on [0,2]. Find the right Riemann sum relative to the regular partitions P2, P3, P4. From this these three approximations, could you guess what is the area of the region bounded by y = 3x - x² and the x-axis on [0,2]? 2. Let f(x) = be defined on [0,1]. Find the left, right, and midpoint Riemann sums relative to the regular partitions P₂ and P3. x+1 3. Let f(x) =tan tan x defined on [0, π/4]. Find the left, right, and midpoint Riemann sums relative to the regular partitions P₂ and P3.
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