Line integrals can look a lot alike! But they represent very different things. Consider: (ii) S¹ (i) Jot f ds [F. F. dr (iii) [F F.nds For each of the above, answer the following questions: a) In words, what does the integral represent? b) Re-write the integral in the form we use to actually evaluate it (i.e. functions of t everywhere) c) For (ii) and (iii), re-write the integral in “scalar differential form." This is the form involving M, N, P and dx, dy, dz.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Line integrals can look a lot alike! But they represent very different things. Consider:
(ii) Sa
(i)
Jo
f ds
F. dr
(iii) [F.
F.nds
For each of the above, answer the following questions:
a) In words, what does the integral represent?
b) Re-write the integral in the form we use to actually evaluate it (i.e. functions of t everywhere)
c) For (ii) and (iii), re-write the integral in "scalar differential form." This is the form involving
M, N, P and dx, dy, dz.
Transcribed Image Text:Line integrals can look a lot alike! But they represent very different things. Consider: (ii) Sa (i) Jo f ds F. dr (iii) [F. F.nds For each of the above, answer the following questions: a) In words, what does the integral represent? b) Re-write the integral in the form we use to actually evaluate it (i.e. functions of t everywhere) c) For (ii) and (iii), re-write the integral in "scalar differential form." This is the form involving M, N, P and dx, dy, dz.
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