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(a) Evaluate as a signed area La (b) Using (a) prove that the limit lim nxn (1 + 2x) dx n 8 -3+ i = 4. n i=1 by expressing the limit of the sum as a definite integral on the interval [-2,2]. (c) Using (a), calculate the average value of f(x) = (1 + 2x) over [-2,2].

(a) Evaluate as a signed area La (b) Using (a) prove that the limit lim nxn (1 + 2x) dx n 8 -3+ i = 4. n i=1 by expressing the limit of the sum as a definite integral on the interval [-2,2]. (c) Using (a), calculate the average value of f(x) = (1 + 2x) over [-2,2].

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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Please answer all questions which are a, b and (c)

(a) Evaluate as a signed area (1 + 2x)dx -2 (b) Using (a) prove that the limit lim n→∞ N -2 n 4 8 −3+ i = 4. n i=1 by expressing the limit of the sum as a definite integral on the interval [-2,2]. (c) Using (a), calculate the average value of f(x) = = (1 + 2x) over [-2,2].
Transcribed Image Text:(a) Evaluate as a signed area (1 + 2x)dx -2 (b) Using (a) prove that the limit lim n→∞ N -2 n 4 8 −3+ i = 4. n i=1 by expressing the limit of the sum as a definite integral on the interval [-2,2]. (c) Using (a), calculate the average value of f(x) = = (1 + 2x) over [-2,2].
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