Line Integrals Let F ( x , y ) = 2 x i + x y 2 j and consider the curve y = x 2 from ( 0 , 0 ) to ( 2 , 4 ) in the xy -plane. Set up and evaluate line integrals of the forms ∫ C F · d r and ∫ C M d x + N d y . Compare your results. Which method do you prefer? Explain.
Line Integrals Let F ( x , y ) = 2 x i + x y 2 j and consider the curve y = x 2 from ( 0 , 0 ) to ( 2 , 4 ) in the xy -plane. Set up and evaluate line integrals of the forms ∫ C F · d r and ∫ C M d x + N d y . Compare your results. Which method do you prefer? Explain.
Let
F
(
x
,
y
)
=
2
x
i
+
x
y
2
j
and consider the curve
y
=
x
2
from
(
0
,
0
)
to
(
2
,
4
)
in the xy-plane. Set up and evaluate line integrals of the forms
∫
C
F
·
d
r
and
∫
C
M
d
x
+
N
d
y
. Compare your results. Which method do you prefer? Explain.
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.
(b) Evaluate the line integral
Jo dzalong the simple
closed contour C shown in
the diagram.
-2 -1
2j
o
1
2
Evaluate This Integral
if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to point (2,4) and curve C₂ which is a vertical line segment from point (2,4) to point (2,6) if a and b are each constant.
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