In this problem you will calculate | 3x dx by using the formal definition of the definite integral: n f(x) dx lim E f(x)A. %3D n-00 k=1 (a) The interval [0, 3] 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 3 3x dx = lim E f(x;)Ax n-00 k=1 What is f(x)Ax (in terms of k and n)? f(xt)Ax = (d) Express f(x)Ax in closed form. (Your answer will be in terms of n.) k=1 n E f(xt)Ax = k=1 (e) Finally, complete the problem by taking the limit as n → o of the expression that you found in the previous part. 3 3x dx = lim E f(x;)Ax %3D n-00 k=1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3
In this problem you will calculate
3x' dx by using the formal definition of the definite integral:
f(x) dx
= lim
E f(x;)Ax
n→00
k=1
(a) The interval [0, 3] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)?
Дх -
(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
3
n
3x dx = lim E f(x;)Ax
k=1
What is f(x)Ax (in terms of k and n)?
f(x#)Ax =
%3D
n
(d) Express f(x)Ax in closed form. (Your answer will be in terms of n.)
k=1
n
Ë f(x})Ax =
k=1
(e) Finally, complete the problem by taking the limit as n → o∞ of the expression that you found in the previous part.
3
3x dx =lin | Σ f()Δx
=
k=1
Transcribed Image Text:3 In this problem you will calculate 3x' dx by using the formal definition of the definite integral: f(x) dx = lim E f(x;)Ax n→00 k=1 (a) The interval [0, 3] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)? Дх - (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 3 n 3x dx = lim E f(x;)Ax k=1 What is f(x)Ax (in terms of k and n)? f(x#)Ax = %3D n (d) Express f(x)Ax in closed form. (Your answer will be in terms of n.) k=1 n Ë f(x})Ax = k=1 (e) Finally, complete the problem by taking the limit as n → o∞ of the expression that you found in the previous part. 3 3x dx =lin | Σ f()Δx = k=1
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