SUORUME 2010 on 01852 31 19-22 Evaluate the line integral je F. dr, where C is given by the vector function r(t). 19. F(x, y) = xy²i – x² j, r(t) = t³i+t²j, 0≤ t ≤1 20. F(x, y, z) = (x + y²)i + xzj + (y+z)k, r(t) = t² i + t³j - 2tk, 0≤ t ≤2 21. F(x, y, z) = sin xi + cos y j + xzk, r(t) = t³i- t² i + tk 0≤t≤1 CAS 32. (a) Find F(x, arou clock (b) Use and your 33. A thin w x² + y² find the
SUORUME 2010 on 01852 31 19-22 Evaluate the line integral je F. dr, where C is given by the vector function r(t). 19. F(x, y) = xy²i – x² j, r(t) = t³i+t²j, 0≤ t ≤1 20. F(x, y, z) = (x + y²)i + xzj + (y+z)k, r(t) = t² i + t³j - 2tk, 0≤ t ≤2 21. F(x, y, z) = sin xi + cos y j + xzk, r(t) = t³i- t² i + tk 0≤t≤1 CAS 32. (a) Find F(x, arou clock (b) Use and your 33. A thin w x² + y² find the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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18. The figure shows a vector field F and two curves C₁ and C₂.
Are the line integrals of F over C₁ and C₂ positive, negative,
or zero? Explain. 10
19. F(x, y) = xy²i - x² j,
.
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f
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r(t) = t³i+t²j, 0≤t≤1
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1
1 1
C₂1
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7
→→
19-22 Evaluate the line integral e F dr, where C is given by
the vector function r(t).
21. F(x, y, z) = sin xi + cos y j + xz k,
r(t) = t³i- t²j + tk, 0≤ t ≤ 1
X
>→→→→
20. F(x, y, z) = (x + y²)i + xz j + (y + z) k,
r(t) = t²i+t³j2tk, 0≤t≤2
X
22. F(x, y, z) = xi+yj + xyk,
r(t) = cos ti+ sin tj + tk, 0≤t≤ T
23-26 Use a calculator to evaluate the line integral correct to
four decimal places.
23. F. dr, where F(x, y) = √√x+yi+ (y/x) j and
r(t) = sin²ti+ sint cos tj, π/6 ≤ t ≤ π/3
he line inte
or zero. Then evaluate the
27. F(x, y) = (x - y)i +
C is the arc of the circ
clockwise from (2, 0)
28. F(x, y)
X
√√x² + y²
C is the parabola y =
=
29. (a) Evaluate the line
F(x, y) = e¹i
r(t) = t²i+t³j
CAS
(b) Illustrate part (a)
puter to graph C
corresponding to
30. (a) Evaluate the line
F(x, y, z) = xi
r(t) = 2ti+ 3:
(b) Illustrate part (a
the vectors from
t = ±1 and ±
CAS 31. Find the exact value
with parametric equ
z=e¹, 0≤t≤2
32. (a) Find the work
F(x, y) = x²i
around the circ
clockwise dire
(b) Use a compute
and circle on t
your answer to
33. A thin wire is bent
x² + y² = 4₁ x >
find the mass and
34. A thin wire has th
circle with center
function is p(x, y)
of the wire.
35. (a) Write the form
of mass (x, y
curve C if the
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