In Section 5.1 we discussed three common ways to pick the ck values: right-hand endpoints, left-hand endpoints, and midpoints. The intervals are [a₁a+b=a]. [a+ a, n b-a Therefore n a + 2(b-a) =a)]. [a + 2(b-a). n n a + n a + S = 2(b − a) where we note that the end of the last interval simplifies to b. With right-hand endpoints, this means the C values are b-a n ,a+ -, a + 3(b-a) .... a. a)], + n 3(b- a) n ..a + n b-a b = ² Σ1 (a + k(b-a) n k=1 (n-1)(b-a) n +k(b=a)). ,a+ n(b-a) n =)] n(ba) n Task 2: Write down similar expressions for the Riemann sum using left-hand endpoints, and midpoints.
In Section 5.1 we discussed three common ways to pick the ck values: right-hand endpoints, left-hand endpoints, and midpoints. The intervals are [a₁a+b=a]. [a+ a, n b-a Therefore n a + 2(b-a) =a)]. [a + 2(b-a). n n a + n a + S = 2(b − a) where we note that the end of the last interval simplifies to b. With right-hand endpoints, this means the C values are b-a n ,a+ -, a + 3(b-a) .... a. a)], + n 3(b- a) n ..a + n b-a b = ² Σ1 (a + k(b-a) n k=1 (n-1)(b-a) n +k(b=a)). ,a+ n(b-a) n =)] n(ba) n Task 2: Write down similar expressions for the Riemann sum using left-hand endpoints, and midpoints.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Task 2: Write down similar expressions for the Riemann sum using left-hand endpoints, and midpoints. A picture of the possible answer options is also provided.
Transcribed Image Text:α(k + 1) + Δε
α
+ (k - 1)Δα
a + (k + 1)Δα
a+kΔυ
α(k - 1) + Δι
ak + Δα
![In Section 5.1 we discussed three common ways to pick the Ck values: right-hand endpoints, left-hand endpoints,
and midpoints. The intervals are
b-a
a +
[a, a + b = a]. [a
n
n
Therefore
-, a +
2(6
a +
- a
n
22]. [₁
b-a
n
, a +
a +
2(b- - a)
n
where we note that the end of the last interval simplifies to b. With right-hand endpoints, this means the ck
values are
S
2(ba)
n
-, a +
a
-3(6-0) ) [ ₁ + (n − 1)(b − a),
.....
a
n
n
n
₂a +
k=1
3(b- a)
b a
k(b-a)
*=*=-=-² (a + (-²²).
n
n
n
1,..., a +
n(b - a)
,a +
n
n(b
a
="2].
n
Task 2: Write down similar expressions for the Riemann sum using left-hand endpoints, and midpoints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ce5a312-47f5-4ea5-9943-a91071c93119%2Fbe8c2f38-ea72-4eb9-919d-93d66ee35fa6%2Fmjgl5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Section 5.1 we discussed three common ways to pick the Ck values: right-hand endpoints, left-hand endpoints,
and midpoints. The intervals are
b-a
a +
[a, a + b = a]. [a
n
n
Therefore
-, a +
2(6
a +
- a
n
22]. [₁
b-a
n
, a +
a +
2(b- - a)
n
where we note that the end of the last interval simplifies to b. With right-hand endpoints, this means the ck
values are
S
2(ba)
n
-, a +
a
-3(6-0) ) [ ₁ + (n − 1)(b − a),
.....
a
n
n
n
₂a +
k=1
3(b- a)
b a
k(b-a)
*=*=-=-² (a + (-²²).
n
n
n
1,..., a +
n(b - a)
,a +
n
n(b
a
="2].
n
Task 2: Write down similar expressions for the Riemann sum using left-hand endpoints, and midpoints.
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