Produce an approximation of its antiderivative function, FA: (t), Gat(t), and HA: (t) for an arbitrary At on the interval [to = 0, tn]. Your answers should include the first four At-intervals, followed by vertical dots, and the nth At-interval. In other words, if J(t) is an antiderivative for j(t) and J(0) = C, then %3D C + j(to)(t – to) C + j(to)At + j(tı)(t – t1) C+ j(to)At + j(t1)At + j(t2)(t – t2) on Atį = [to,t1] on At, = [t1, t2] on Atz = [t2,t3] Ja: (t) = C+ (E j(tn-1)At) + j(tn)(t – tn) on At, = [tn-1, tn] i=1
Produce an approximation of its antiderivative function, FA: (t), Gat(t), and HA: (t) for an arbitrary At on the interval [to = 0, tn]. Your answers should include the first four At-intervals, followed by vertical dots, and the nth At-interval. In other words, if J(t) is an antiderivative for j(t) and J(0) = C, then %3D C + j(to)(t – to) C + j(to)At + j(tı)(t – t1) C+ j(to)At + j(t1)At + j(t2)(t – t2) on Atį = [to,t1] on At, = [t1, t2] on Atz = [t2,t3] Ja: (t) = C+ (E j(tn-1)At) + j(tn)(t – tn) on At, = [tn-1, tn] i=1
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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Question
Consider the 3 examples
- f ( t ) = 60, F ( 0 ) = 0
- g ( t ) = 10 − 2 t, G ( 0 ) = 0
- h ( t ) = sin ( t ), H(0) = -1
![f(t) = 60, F(0) = 0
g(t) = 10 – 2t, G(0) = 0
h(t) = sin(t), H(0) = –1
Problems
1. Produce an approximation of its antiderivative function, FAt (t), GA:(t), and Ha:(t) for an
arbitrary At on the interval [to = 0, tn]. Your answers should include the first four At-intervals,
followed by vertical dots, and the nth At-interval. In other words, if J(t) is an antiderivative for
j(t) and J(0) = C, then
C+ j(to)(t – to)
C + j(to)At + j(t1)(t – ti)
C + j(to)At + j(tı)At + j(t2)(t – t2)
on At¡ = [to,t1]
on At, = [t1, t2]
on Atz = [t2, t3]
-
Jat (t)
C+ (E j(n-1)At) + j(tn)(t – tm) on At, = [tn-1, tn]
vi=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08c320b2-b994-4f70-a811-3e06f114cb55%2F2940658a-8274-4b80-9f77-caa945ee5bf9%2F1y1uvi_processed.png&w=3840&q=75)
Transcribed Image Text:f(t) = 60, F(0) = 0
g(t) = 10 – 2t, G(0) = 0
h(t) = sin(t), H(0) = –1
Problems
1. Produce an approximation of its antiderivative function, FAt (t), GA:(t), and Ha:(t) for an
arbitrary At on the interval [to = 0, tn]. Your answers should include the first four At-intervals,
followed by vertical dots, and the nth At-interval. In other words, if J(t) is an antiderivative for
j(t) and J(0) = C, then
C+ j(to)(t – to)
C + j(to)At + j(t1)(t – ti)
C + j(to)At + j(tı)At + j(t2)(t – t2)
on At¡ = [to,t1]
on At, = [t1, t2]
on Atz = [t2, t3]
-
Jat (t)
C+ (E j(n-1)At) + j(tn)(t – tm) on At, = [tn-1, tn]
vi=1
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