Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 35. ∮ C ( 2 x + e y 2 ) d x − ( 4 y 2 + e x 2 ) d x , where C is the boundary of the rectangle with vertices (0, 0) (1, 0) (1, 1) and (0, 1)
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 35. ∮ C ( 2 x + e y 2 ) d x − ( 4 y 2 + e x 2 ) d x , where C is the boundary of the rectangle with vertices (0, 0) (1, 0) (1, 1) and (0, 1)
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
35.
∮
C
(
2
x
+
e
y
2
)
d
x
−
(
4
y
2
+
e
x
2
)
d
x
, where C is the boundary of the rectangle with vertices (0, 0) (1, 0) (1, 1) and (0, 1)
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 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.
(b) Evaluate the line integral
Jo dzalong the simple
closed contour C shown in
the diagram.
-2 -1
2j
o
1
2
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