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1) Let f(x) = 1 – x² on [-1,2]. Find L(P, f) and U(P, f) for P = {-1,0, 1, 2}.

1) Let f(x) = 1 – x² on [-1,2]. Find L(P, f) and U(P, f) for P = {-1,0, 1, 2}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Let f(x) = 1 – x² on [-1,2]. Find L(P, f) and U(P, f) for P = {-1,0, 1, 2}. | 0, a <x < c, Show that f e R[a, b] and find S" f. (b) Let f(x) = 1 x = c, 2 1, c<x < b. (c) Let f(x) = 2x +1 on [0, 1]. Show that f e R[0, 1] and find So f.
Transcribed Image Text:(a) Let f(x) = 1 – x² on [-1,2]. Find L(P, f) and U(P, f) for P = {-1,0, 1, 2}. | 0, a <x < c, Show that f e R[a, b] and find S" f. (b) Let f(x) = 1 x = c, 2 1, c<x < b. (c) Let f(x) = 2x +1 on [0, 1]. Show that f e R[0, 1] and find So f.
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