Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 29. ∮ C x y 2 d x + x 2 y d y ; C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 29. ∮ C x y 2 d x + x 2 y d y ; C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
Solution Summary: The author evaluates the value of the line integral displaystyleundersetCoint.
Green’s Theorem for line integralsUse either form of Green’s Theorem to evaluate the following line integrals.
29.
∮
C
x
y
2
d
x
+
x
2
y
d
y
;
C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Evaluate
C
F · dr
using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.
(2yi
C
+ 2xj) · dr
C: smooth curve from (0, 0) to (2, 3)
Please explain each step. I am getting confused.
Evaluate
F · dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify
your results.
(2z + 4y) dx + (4x – 3z) dy + (2x – 3y) dz
(a)
C: line segment from (0, 0, 0) to (1, 1, 1)
(b)
C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1)
(c)
C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)
Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx, cosx >
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