Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 37. ∮ C f d y − g d x where 〈 f , g 〉 = 〈 0 , x y 〉 and C is the triangle with vertices (0, 0) (2, 0) and (0, 4)
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 37. ∮ C f d y − g d x where 〈 f , g 〉 = 〈 0 , x y 〉 and C is the triangle with vertices (0, 0) (2, 0) and (0, 4)
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
37.
∮
C
f
d
y
−
g
d
x
where
〈
f
,
g
〉
=
〈
0
,
x
y
〉
and C is the triangle with vertices (0, 0) (2, 0) and (0, 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.
Find the slope of the tangent in the positive x-direction to the surface z =
3x3 – 6xy at the point (2, 1, 12).
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sin x
Evaluate the line integral S, F · dr, where F(x, y) =
positively oriented triangle with vertices at (0,0), (1, 1), and (-2,1). Sketch the
sinz
i- xy j and C is the
curve.
Use Green's theorem to evaluate
F. dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x)), Cis the triangle from (0, 0) to (0, 10) to (2, 0) to (0, 0)
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