Consider decreasing function f(x) = 1 + x3 on interval [0,1]. Use upper Riemann sum, with partition P = {0, 1/2, 1}, to show that: S²₁ da 1+x³ 17 18

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider decreasing function f(x)
=
1 + x3
on interval [0,1].
Use upper Riemann sum, with partition P = {0, 1/2, 1}, to show that:
S²₁
da
1+x³
17
18
Transcribed Image Text:Consider decreasing function f(x) = 1 + x3 on interval [0,1]. Use upper Riemann sum, with partition P = {0, 1/2, 1}, to show that: S²₁ da 1+x³ 17 18
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I did not understand why integral is less than 17/18. I see you have calculated integral for both extremes but you get 17/18. How do I check it? You would have to calculate integral for both ends (upper and lower) to check.
Can you explain better? Thanks

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