Line integrals use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 39. The circulation line integral of F = 〈 x 2 + y 2 , 4 x + y 3 〉 where C is boundary of {( x, y ) : 0 ≤ y ≤ sin x , 0 ≤ x ≤ π}
Line integrals use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 39. The circulation line integral of F = 〈 x 2 + y 2 , 4 x + y 3 〉 where C is boundary of {( x, y ) : 0 ≤ y ≤ sin x , 0 ≤ x ≤ π}
Line integrals use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
39. The circulation line integral of F =
〈
x
2
+
y
2
,
4
x
+
y
3
〉
where C is boundary of {(x, y) : 0 ≤ y ≤ sin x, 0 ≤ x ≤ π}
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.
ulus III
|Uni
Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along
CoS
the positively oriented curve C, where C is the rectangle with vertices(0,0), (4, 0), (4, 2) and (0, 2).
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.
3 In(3 + y) dx -
-dy, where C is the triangle with vertices (0,0), (6, 0), and (0, 12)
ху
3+y
ху
dy =
3 In(3 + y) dx -
3+ y
Use Green's Theorem to evaluate the
integral. Assume that the curve Cis oriented
counterclockwise.
6 In(6+ y) dx
ху
dy, where C is
6+ y
C
the triangle with vertices (0, 0), (3,0), and
(0, 6)
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