In this problem you will calculate x +5 dx by using the formal definition of the definite integral: f(x) dx = lim E f(xt)Ax n+00 k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax = (b) The right-hand endpoint of the kth subinterval is denoted x. What is x (in terms of k and n)? (c) Using these choices for x and Ax, the definition tells us that x² +5 dx = limE f(x;)A> n00 k=1 What is f(xt)Ax (in terms of k and n)? f(x)Ax = (d) Express E f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 E f(x;)Ax = k=1 (e) Finally, complete the problem by taking the limit as n → ∞ of the expression that you found in the previous part. x? + 5 dx = lim E f(x;)Ax = n+00 k=1
In this problem you will calculate x +5 dx by using the formal definition of the definite integral: f(x) dx = lim E f(xt)Ax n+00 k=1 (a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Ax = (b) The right-hand endpoint of the kth subinterval is denoted x. What is x (in terms of k and n)? (c) Using these choices for x and Ax, the definition tells us that x² +5 dx = limE f(x;)A> n00 k=1 What is f(xt)Ax (in terms of k and n)? f(x)Ax = (d) Express E f(x;)Ax in closed form. (Your answer will be in terms of n.) k=1 E f(x;)Ax = k=1 (e) Finally, complete the problem by taking the limit as n → ∞ of the expression that you found in the previous part. x? + 5 dx = lim E f(x;)Ax = n+00 k=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![In this problem you will calculate
x +5 dx by using the formal definition of the definite integral:
f(x) dx = lim E f(xt)Ax
n+00
k=1
(a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)?
Ax =
(b) The right-hand endpoint of the kth subinterval is denoted x. What is x (in terms of k and n)?
(c) Using these choices for x and Ax, the definition tells us that
x² +5 dx = limE f(x;)A>
n00
k=1
What is f(xt)Ax (in terms of k and n)?
f(x)Ax =
(d) Express E f(x;)Ax in closed form. (Your answer will be in terms of n.)
k=1
E f(x;)Ax =
k=1
(e) Finally, complete the problem by taking the limit as n → ∞ of the expression that you found in the previous part.
x? + 5 dx = lim
E
f(x;)Ax =
n+00
k=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94f0d779-bbe1-4b79-9146-48c3267c31db%2F30670f8f-3b95-4234-bf5a-2ce0ed2dffe5%2Fny9hsz_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem you will calculate
x +5 dx by using the formal definition of the definite integral:
f(x) dx = lim E f(xt)Ax
n+00
k=1
(a) The interval [0, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)?
Ax =
(b) The right-hand endpoint of the kth subinterval is denoted x. What is x (in terms of k and n)?
(c) Using these choices for x and Ax, the definition tells us that
x² +5 dx = limE f(x;)A>
n00
k=1
What is f(xt)Ax (in terms of k and n)?
f(x)Ax =
(d) Express E f(x;)Ax in closed form. (Your answer will be in terms of n.)
k=1
E f(x;)Ax =
k=1
(e) Finally, complete the problem by taking the limit as n → ∞ of the expression that you found in the previous part.
x? + 5 dx = lim
E
f(x;)Ax =
n+00
k=1
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