In this problem you will calculate 2x dx by using the formal definition of the definite integral: f(x) dx n-00 k=1 (a) The interval [2, 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)?
In this problem you will calculate 2x dx by using the formal definition of the definite integral: f(x) dx n-00 k=1 (a) The interval [2, 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)?
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In this problem you will calculate
2x dx by using the formal definition of the definite integral:
n
f(x) dx = limIE f(x*)Ax
k=1
(a) The interval [2, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)?
Ax
%D
(b) The right-hand endpoint of the kth subinterval is denoted x*. What is x* (in terms of k and n)?
%3D
(c) Using these choices for x* and Ax, the definition tells us that
4
n
2х dx —D lim
E f(x;)Ax
k=1
What is f(x)Ax (in terms of k and n)?
f(x)Ax =
n
(d) Express E f(x*)Ax in closed form. (Your answer will be in terms of n.)
k=1
n
E 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.
4
n
2х dx
lim Ef(x)Ax
%D
k=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdab71e2a-a9b1-410a-af21-6f59e3c039d4%2Fee1ced7b-c31a-42ec-b0b7-879ed32bc084%2Fhp1b57q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4
In this problem you will calculate
2x dx by using the formal definition of the definite integral:
n
f(x) dx = limIE f(x*)Ax
k=1
(a) The interval [2, 4] is divided into n equal subintervals of length Ax. What is Ax (in terms of n)?
Ax
%D
(b) The right-hand endpoint of the kth subinterval is denoted x*. What is x* (in terms of k and n)?
%3D
(c) Using these choices for x* and Ax, the definition tells us that
4
n
2х dx —D lim
E f(x;)Ax
k=1
What is f(x)Ax (in terms of k and n)?
f(x)Ax =
n
(d) Express E f(x*)Ax in closed form. (Your answer will be in terms of n.)
k=1
n
E 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.
4
n
2х dx
lim Ef(x)Ax
%D
k=1
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