Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 29. ∮ C x y 2 d x + x 2 y d y ; C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
Green’s Theorem for line integrals Use either form of Green’s Theorem to evaluate the following line integrals. 29. ∮ C x y 2 d x + x 2 y d y ; C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
Solution Summary: The author evaluates the value of the line integral displaystyleundersetCoint.
Green’s Theorem for line integralsUse either form of Green’s Theorem to evaluate the following line integrals.
29.
∮
C
x
y
2
d
x
+
x
2
y
d
y
;
C is the triangle with vertices (0, 0), (2, 0), and (0, 2) with counterclockwise orientation.
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.
1.Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if F→(x,y)=(10x+10y)i→+(10x+10y)j→and Cis the smooth curve from (−1,1)to (8,9).
Enter the exact answer.
∫CF→⋅dr→
Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if F→(x,y)=(4x+4y)i→+(4x+4y)j→and Cis the smooth curve from (−1,1)to (5,6).
Enter the exact answer.
∫CF→⋅dr→=
Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.3. ∮C xy dx + x2y3 dy,C is the triangle with vertices (0, 0), (1, 0), and (1, 2)
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