[T] Evaluate Green’s theorem using a computer algebra system to evaluate the integral ∫ c x e y d x + e x d y , where C is the circle given by x + y = 4 and is oriented in the counterclockwise direction.
[T] Evaluate Green’s theorem using a computer algebra system to evaluate the integral ∫ c x e y d x + e x d y , where C is the circle given by x + y = 4 and is oriented in the counterclockwise direction.
[T] Evaluate Green’s theorem using a computer algebra system to evaluate the integral
∫
c
x
e
y
d
x
+
e
x
d
y
,
where C is the circle given by x + y = 4 and is oriented in the counterclockwise direction.
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.
Let F = (7z+7x4) 7 + (3y + 2z + 2 sin (14)) 7 + (7x + 2y + 3e²¹ ) k.
(a) Find curl F.
curl F =
(b) What does your answer to part (a) tell you about F. dr where C is the circle
(x - 20)² + (y - 15)² = 1 in the xy-plane, oriented clockwise?
JcF. dr =
(c) If C is any closed curve, what can you say about F. dr?
F. dr =
(d) Now let C be the half circle (x - 20)² + (y − 15)² = 1 in the xy-plane with y > 15, traversed
from (21, 15) to (19, 15). Find F. dr by using your result from (c) and considering C plus the
line segment connecting the endpoints of C.
JcF. dr =
Use Green's Theorem to evaluate
|v - In(x2 + y²))dx + 2 tan-(y/x) dy,
C is the circle (x – 4)² + (y – 3)² = 4 oriented counterclockwise.
(a) Let f(2) =
24 + 5z3
Evaluate the integral Of(2)dz, where the contour C is the circle z = 2.
Finite Mathematics & Its Applications (12th Edition)
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