Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C x 2 − y d x + x d y , where C is the circle x 2 + y 2 = 4.
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C x 2 − y d x + x d y , where C is the circle x 2 + y 2 = 4.
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise.
∮
C
x
2
−
y
d
x
+
x
d
y
,
where C is the circle
x
2
+
y
2
=
4.
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 (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9 with positive direction using Green's Theorem.
Evaluate the line integral
(3ry² + 6y) dr, where C is the path traced by first moving from the
point (-3, 1) to the point (2, 1) along a straight line, then moving from the point (2, 1) to the
point (5,2) along the parabola x = y² + 1.
Evaluate
| 2*(x + 7) – 2y ds
where C is the circle of radius 1 centered at (-3,0) and lying on the plane x = -3.
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