Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C cos x sin y d x + sin x cos y d y , where C is the triangle with vertices (0, 0),(3, 3), and (0, 3) .
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C cos x sin y d x + sin x cos y d y , where C is the triangle with vertices (0, 0),(3, 3), and (0, 3) .
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise.
∮
C
cos
x
sin
y
d
x
+
sin
x
cos
y
d
y
,
where C is the triangle with vertices
(0,
0),(3,
3), and (0,
3)
.
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.
Determine order and degree *
d'y
+ cos
dr?
d'y
dr?
2
O 5
undefine- Not linear
Write an equation for a line that passes through the points (1,-1) and (5,7)
Q 2.
Let C₁ be the straight line from the point (1,0) to the point (0, 1) in Figure 1. Let C₂ be an
oriented and closed path in Figure 1.
(a)
(b)
Evaluate the line integral of F = 4xi + 2xj along C₁.
Evaluate the line integral of F = sin(2x)i + ej along C₂.
Figure 1: A closed and oriented path
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