Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 38. ∮ c f d y − g d x where 〈 f , g 〉 = 〈 x 〉 and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 38. ∮ c f d y − g d x where 〈 f , g 〉 = 〈 x 〉 and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
38.
∮
c
f
d
y
−
g
d
x
where
〈
f
,
g
〉
=
〈
x
〉
and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
(b) Evaluate the line integral
Jo dzalong the simple
closed contour C shown in
the diagram.
-2 -1
2j
o
1
2
Use Green's Theorem to evaluate F · dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) = sqrtx+ 4y3, 4x2 + sqrty
C consists of the arc of the curve y = sin(x) from (0, 0) to (π, 0) and the line segment from (π, 0) to (0, 0)
Name:
Fincling the derivative of trig
gonometric
fox)= aln (2+ J
Chapter 17 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
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