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.
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
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).
Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.
(3yi + 3xj) · dr
C: smooth curve from (0, 0) to (3, 7)
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