Math 2433
Section 26013
MW 1-2:30pm GAR 205
Bekki George
[email protected]
639 PGH
Office Hours:
11:00 - 11:45am MWF or by appointment
17.4 Line Integrals in Different Notation
Given a vector function h(x, y) = P(x, y)i + Q(x, y)j
and a curve C: r(u) = x(u)i + y(u)j, a ≤ u ≤ b
then
∫
C
h(r) ⋅dr = ∫ P(x, y) dx + Q(x, y) dy
C
Example:
1. Find
∫ h(r) i dr
C
2
2
3
h(x,
y)
=
x
y
i
+
2xy
j
r(u)
=
u
i
+
(1−
u
)j, 0 ≤ u ≤ 2
given
and
2. Evaluate: ∫ (x − 2y)dx + 2x dy along the parabolic path C: y = 2x2 from (0,0) to
C
(1,2)
Exam Review:
Popper20
1.Evaluate ∫ y dx + xy dy along the cubic path C from (0,0) to (5,1) along
C
x = 5y3.
2
4−y 2
2.Convert ∫ ∫
0
4−x 2 −y 2
0
∫
x 2 + y 2 dz dx dy into
0
coordinates.
u+v
x=
2
3.Given
of u and v.
and y =
an integral with spherical
u−v
2 , re-write the following integral in terms
Ω : 0 ≤ x − y ≤ 2, 1 ≤ x + y ≤ 4
∫∫ 2xy dx dy
4.Set h(x, y) = ( 2xy + 3x + 2 ) i + ( 2x y − 2y + 1) j and
C : r(u) = 2u i + ( u + 2 ) j, 0 ≤ u ≤ 1
Ω
2
2
∫
C
h(r)⋅ dr =
3
2
2