Evaluating a Line Integral in Differential Form In Exercises 53-56, evaluate the line integral along the path C given by x = 2 t , y = 4 t , where 0 ≤ t ≤ 1 . ∫ C ( y − x ) d x + 5 x 2 y 2 d y
Evaluating a Line Integral in Differential Form In Exercises 53-56, evaluate the line integral along the path C given by x = 2 t , y = 4 t , where 0 ≤ t ≤ 1 . ∫ C ( y − x ) d x + 5 x 2 y 2 d y
Solution Summary: The author explains how the line integral displaystyleundersetCint is 258.
Evaluating a Line Integral in Differential Form In Exercises 53-56, evaluate the line integral along the path C given by
x
=
2
t
,
y
=
4
t
,
where
0
≤
t
≤
1
.
∫
C
(
y
−
x
)
d
x
+
5
x
2
y
2
d
y
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.
Using the Hough transform i) Develop a general procedure for obtaining the normal representation of a line from its slope-intercept form, y = ax + b. ii) Find the normal representation of the line y = – 2x + 1.
Complex variables
Application of Green's theorem
Assume that u and u are continuously differentiable functions. Using Green's theorem,
prove that
JS
D
Ur
Vy
dA=
u dv,
where D is some domain enclosed by a simple closed curve C with positive orientation.
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