57095-15-47RE-Question-Digital.docx Evaluating a Line Integral In Exercises 45–50, use Green’s Theorem to evaluate the line integral. ∫ C x y 2 d x + x 2 y d y C : x = 4 cos t , y = 4 sin t
Solution Summary: The author explains how the fundamental theorem of Line Integrals states that a piecewise smooth curve C lying in an open region R is provided by r(t)=xstack
Evaluating a Line Integral In Exercises 45–50, use Green’s Theorem to evaluate the line integral.
∫
C
x
y
2
d
x
+
x
2
y
d
y
C
:
x
=
4
cos
t
,
y
=
4
sin
t
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.
A) Evaluate the given line integral directly. B) Evaluate the given line integral by using Green's theorem.
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→=
Using green's theorem, evaluate the line integral xy^2dx + (1-xy^3)dy
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