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 + y + x y 2 d y , where C is the boundary of the region enclosed by y = x 2 and x = y 2 .
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 + y + x y 2 d y , where C is the boundary of the region enclosed by y = x 2 and x = y 2 .
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
+
y
+
x
y
2
d
y
,
where C is the boundary of the region enclosed by
y
=
x
2
and
x
=
y
2
.
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 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 line integral f,dr where f=(x2+y2)i and c is the rectangle in the xy plane bounded by x=0,x=a,y=b and y=0
Use Green's Theorem to evaluate the line integral of F = (x6, 3x)
around the boundary of the parallelogram in the following figure (note the orientation).
(xo.)
(X0.0)
Sex6 dx + 3x dy
=
(2x-Y)
·x
With xo =
7 and yo
=
7.
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