Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C e x + y 2 d x + e y + x 2 d y , where C is the boundary of the region between y = x 2 and y = x .
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise. ∮ C e x + y 2 d x + e y + x 2 d y , where C is the boundary of the region between y = x 2 and y = x .
Use Green’s Theorem to evaluate the integral. In each exercise, assume that the curve C is oriented counterclockwise.
∮
C
e
x
+
y
2
d
x
+
e
y
+
x
2
d
y
,
where C is the boundary of the region between
y
=
x
2
and
y
=
x
.
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 f(2x-y+6)dx + (5y + 3x-6)dy, for which the path C traverses
around a circle of radius 2 with centre at (0, 0) in the counterclockwise direction.
Answer:
(Round
Evaluate This Integral
if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to point (2,4) and curve C₂ which is a vertical line segment from point (2,4) to point (2,6) if a and b are each constant.
Evaluate
fot F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.
JC
1 [8(4x + 5y)i + 10(4x + 5y)j] · dr
C: smooth curve from (-5, 4) to (3, 2)
X
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