32. a. + 2n b. с. k=1 50
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![in values generated
5.3 The Definite Integral
317
32. a.
+2n
b.
k=1
C.
33. [(k + 1)² – k²]
34. [ sin (k - 1) sin k]
k=1
20.
k=2
35. (Vk - 4 - Vk - 3)
k=7
ht Theorem
1.
k(k + 1)
40
1.
Hint:
k (k + 1)
kk + 1
The
Variable
(4-1-
Riemann Sums
aghout a
In Exercises 37-42, graph each function f(x) over the given interval.
Partition the interval into four subintervals of equal length. Then add
uous at
to your sketch the rectangles associated with the Riemann sum
=1f(c) Ax, given that c is the (a) left-hand endpoint, (b) right-
hand endpoint, (c) midpoint of the kth subinterval. (Make a separate
sketch for each set of rectangles.)
ano
37. f(x) = x²- 1, [0, 2]
39. f(x)
38. f(x) = -x, [0,1]
|
%3D
sin x, [-T, T]
40. f(x) = sinx + 1, [-m, ]
ne
41. Find the norm of the partition P = {0, 1.2, 1.5, 2.3, 2.6, 3}.
in
%3D
42. Find the norm of the partition P = {-2,-1.6, -0.5, 0, 0.8, 1}.
).
Limits of Riemann Sums
For the functions in Exercises 43-50, find a formula for the Riemann
sum obtained by dividing the interval [a, b] into n equal subintervals
and using the right-hand endpoint for each C. Then take a limit of
these sums as n→∞ to calculate the area under the curve over
1000 sub-
[a, b].
43. f(x) = 1 – x² over the interval [0, 1].
anction at the
|
44. f(x) = 2x over the interval [0, 3].
%3D
45. f(x) = x² + 1 over the interval [0,3].
%3D
46. f(x) = 3x² over the interval [0, 1].
lue) for x using the
%3D
%3D
r the n = 1000 par
47. f(x) = x + x² over the interval [0, 1].
%3D
48. f(x) = 3x + 2r² over the interval [0, 1].
the interval 0, 1 | .
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2001efb4-40b4-4f06-80ad-e82e5c658052%2F3e7ee82b-380f-4ec4-b792-13438efbe5ab%2F7wo5qjd.jpeg&w=3840&q=75)
Transcribed Image Text:in values generated
5.3 The Definite Integral
317
32. a.
+2n
b.
k=1
C.
33. [(k + 1)² – k²]
34. [ sin (k - 1) sin k]
k=1
20.
k=2
35. (Vk - 4 - Vk - 3)
k=7
ht Theorem
1.
k(k + 1)
40
1.
Hint:
k (k + 1)
kk + 1
The
Variable
(4-1-
Riemann Sums
aghout a
In Exercises 37-42, graph each function f(x) over the given interval.
Partition the interval into four subintervals of equal length. Then add
uous at
to your sketch the rectangles associated with the Riemann sum
=1f(c) Ax, given that c is the (a) left-hand endpoint, (b) right-
hand endpoint, (c) midpoint of the kth subinterval. (Make a separate
sketch for each set of rectangles.)
ano
37. f(x) = x²- 1, [0, 2]
39. f(x)
38. f(x) = -x, [0,1]
|
%3D
sin x, [-T, T]
40. f(x) = sinx + 1, [-m, ]
ne
41. Find the norm of the partition P = {0, 1.2, 1.5, 2.3, 2.6, 3}.
in
%3D
42. Find the norm of the partition P = {-2,-1.6, -0.5, 0, 0.8, 1}.
).
Limits of Riemann Sums
For the functions in Exercises 43-50, find a formula for the Riemann
sum obtained by dividing the interval [a, b] into n equal subintervals
and using the right-hand endpoint for each C. Then take a limit of
these sums as n→∞ to calculate the area under the curve over
1000 sub-
[a, b].
43. f(x) = 1 – x² over the interval [0, 1].
anction at the
|
44. f(x) = 2x over the interval [0, 3].
%3D
45. f(x) = x² + 1 over the interval [0,3].
%3D
46. f(x) = 3x² over the interval [0, 1].
lue) for x using the
%3D
%3D
r the n = 1000 par
47. f(x) = x + x² over the interval [0, 1].
%3D
48. f(x) = 3x + 2r² over the interval [0, 1].
the interval 0, 1 | .
%3D
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