Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 32. ∮ C 〈 sin y , x 〉 ⋅ d r , where C is the boundary of the triangle with vertices (0, 0) ( π 2 , 0 ) , 0) and ( π 2 , π 2 )
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 32. ∮ C 〈 sin y , x 〉 ⋅ d r , where C is the boundary of the triangle with vertices (0, 0) ( π 2 , 0 ) , 0) and ( π 2 , π 2 )
Solution Summary: The author evaluates the value of the line integral with the help of Green’s Theorem and sketch a graph.
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
32.
∮
C
〈
sin
y
,
x
〉
⋅
d
r
, where C is the boundary of the triangle with vertices (0, 0)
(
π
2
,
0
)
, 0) and
(
π
2
,
π
2
)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Use Green's Theorem to evaluate F · dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) = sqrtx+ 4y3, 4x2 + sqrty
C consists of the arc of the curve y = sin(x) from (0, 0) to (π, 0) and the line segment from (π, 0) to (0, 0)
F. dr. (Check the orientation of the curve before applying the theorem.)
Jc
Use Green's Theorem to evaluate
F(x, y) = (y2 cos(x), x² + 2y sin(x))
C is the triangle from (0, 0) to (1, 3) to (1, 0) to (0, 0)
²/F 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)), C is the triangle from (0, 0) to (0, 6) to (3, 0) to (0, 0)
Use Green's theorem to evaluate
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