problem.] 5. Suppose that C is a smooth closed curve in R3 given by the vector function r(t), for a . Show that v• dr = v · [r(b) – r(a)). (b) Show that 1 r· dr = -
problem.] 5. Suppose that C is a smooth closed curve in R3 given by the vector function r(t), for a . Show that v• dr = v · [r(b) – r(a)). (b) Show that 1 r· dr = -
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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just need question 5
![4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:
(a
си (х) dx — c(u(b) — и(а), and
(b) / u(z
u(x)u'(x) dz = ¿[u(b)² – u(a)*].
[Hint: This is really straight forward; it does not require anything beyond Calculus I, but is set-up for the next
problem.]
5. Suppose that C is a smooth closed curve in R³ given by the vector function r(t), for a <t < b.
(a) Suppose that v is some constant vector, v =< v1, V2, V3 >. Show that
V• dr
= v · [r(b) – r(a)].
(b) Show that
(c) Now, make a connection back to the results of problem #4 – what similarities and differences do you see?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1863dd2d-66ae-4de0-8154-3d7d6de9d0c9%2Fa09cff1e-e480-48bd-9a7d-8f5dbec621a3%2Fyd5iqi5_processed.png&w=3840&q=75)
Transcribed Image Text:4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:
(a
си (х) dx — c(u(b) — и(а), and
(b) / u(z
u(x)u'(x) dz = ¿[u(b)² – u(a)*].
[Hint: This is really straight forward; it does not require anything beyond Calculus I, but is set-up for the next
problem.]
5. Suppose that C is a smooth closed curve in R³ given by the vector function r(t), for a <t < b.
(a) Suppose that v is some constant vector, v =< v1, V2, V3 >. Show that
V• dr
= v · [r(b) – r(a)].
(b) Show that
(c) Now, make a connection back to the results of problem #4 – what similarities and differences do you see?
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