Student Questions 11-11-14
Would you do a separate review session for the test Monday if there was
enough interest?
This is a great idea but unfortunately for this test it is a little bit too short notice to get
a room reserved and see who is interested. This is most definitely something I will
consider doing before the final exam. Thanks for the idea.
If a line integral does not give the bounds for t, how do you find those?
Good question. One way this would happen is if they say C is the curve given by x = t
and y = t2 from the point (1, 1) to (5, 25). In this case they told us the starting and
ending points but not the bounds for t. So we need to use the points to get our bounds
for t. So looking at the curve, what t value will put us at the point (1, 1)? The answer is
t = 1 because at t = 1, x = 1 and y = 12 = 1. What t value puts us at (5, 25)? The
answer here is t = 5. So we have 1 ≤ t ≤ 5.
R
How do you integrate f (x, y, z)dz?
C
IR think you are getting the two types of integrals confused. If you asked me about
f (x, y, z)ds then this would be the first type of line integral and you would plug the
C
p
3D curve into the function and change ds using ds = x0 (t)2 + y 0 (t)2 + z 0 (t)2 . If you
did mean to write dz then this question still makes sense as the second type of line
integral if the vector field was F~ (x, y, z) = h0, 0, f (x, y, z)i. Then we have
Z
Z
Z
Z
~
~
F · T ds = M dx + N dy + P dz = 0 dx + 0 dy + f (x, y, z) dz = f (x, y, z)dz.
C
C
C
C
In this case you would plug the 3D curve into f (x, y, z) and change dz using dz = z 0 (t)dt.
Can we start having review questions before exams (the final)?
Yes, we should have some time at the end of the semester to review for the final.
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