x26 dxby using the formal definition of the definite integral:In this problem you will calculateC.ebf(x) dx limn-x(a) The interval [0, 2] is divided into N equal subintervals of length Ax. What is Ax (in terms of n)?Ax = 2/n(b) The right-hand endpoint of the kth subinterval is denoted X. What is x(in tems of k and n?2k/n(c) Using these choices for Xand Ax, the definition tells us thatx2 6 dxlimn ooLi-1.f(x)Ax (in terms of k and n)?f(x)Ax = "(2k/n)^2)+6)*(2In)(d) Express(x;)Ax in closed forrm. (Your answer will be in terms of n.)k-1ITHxAx=|k 1(e) Finally, complete the problem by taking the limit as n00 of the expression that you found in the previous part.2x26 dx lim f(xAx44/3nxLk=1

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Asked Oct 11, 2019
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(d) How to express the summation: (x^(2)+6) in closed form? In terms of "n". (domain of 0 to 2)

 

x26 dxby using the formal definition of the definite integral:
In this problem you will calculate
C.
eb
f(x) dx lim
n-x
(a) The interval [0, 2] is divided into N equal subintervals of length Ax. What is Ax (in terms of n)?
Ax = 2/n
(b) The right-hand endpoint of the kth subinterval is denoted X. What is x
(in tems of k and n?
2k/n
(c) Using these choices for X
and Ax, the definition tells us that
x2 6 dx
lim
n oo
Li-1.
f(x)Ax (in terms of k and n)?
f(x)Ax = "(2k/n)^2)+6)*(2In)
(d) Express(x;)Ax in closed forrm. (Your answer will be in terms of n.)
k-1
IT
HxAx=|
k 1
(e) Finally, complete the problem by taking the limit as n
00 of the expression that you found in the previous part.
2
x26 dx lim f(xAx
44/3
nx
Lk=1
help_outline

Image Transcriptionclose

x26 dxby using the formal definition of the definite integral: In this problem you will calculate C. eb f(x) dx lim n-x (a) The interval [0, 2] is divided into N equal subintervals of length Ax. What is Ax (in terms of n)? Ax = 2/n (b) The right-hand endpoint of the kth subinterval is denoted X. What is x (in tems of k and n? 2k/n (c) Using these choices for X and Ax, the definition tells us that x2 6 dx lim n oo Li-1. f(x)Ax (in terms of k and n)? f(x)Ax = "(2k/n)^2)+6)*(2In) (d) Express(x;)Ax in closed forrm. (Your answer will be in terms of n.) k-1 IT HxAx=| k 1 (e) Finally, complete the problem by taking the limit as n 00 of the expression that you found in the previous part. 2 x26 dx lim f(xAx 44/3 nx Lk=1

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Expert Answer

the inegral in the close form and...

f(x)dx limf(x^)(Ax)
2k
and x
where, Ax
n
£«k)2+2;
(x2+6)dx=lim
|
44
3
help_outline

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f(x)dx limf(x^)(Ax) 2k and x where, Ax n £«k)2+2; (x2+6)dx=lim | 44 3

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