Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate ∫ C ( x 2 + y 2 ) d s . C: counterclockwise around the circle x 2 + y 2 = 4 from (2, 0) to ( − 2 , 0 )
Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate ∫ C ( x 2 + y 2 ) d s . C: counterclockwise around the circle x 2 + y 2 = 4 from (2, 0) to ( − 2 , 0 )
Solution Summary: The author calculates a parametrization for the path C that is counterclockwise around the circle x2+y2.
Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate
∫
C
(
x
2
+
y
2
)
d
s
.
C: counterclockwise around the circle
x
2
+
y
2
=
4
from (2, 0) to
(
−
2
,
0
)
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.
Find both parametric and rectangular representations for the plane tangent to r(u,v)=u2i+ucos(v)j+usin(v)kr(u,v)=u2i+ucos(v)j+usin(v)k at the point P(4,−2,0)P(4,−2,0).One possible parametric representation has the form⟨4−4u⟨4−4u , , 4v⟩4v⟩(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the other components should match the ones expected here as well.)The equation for this plane in rectangular coordinates has the form x+x+ y+y+ z+z+ =0
Evaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive
x-axis.
Circulation =
Prevs
So F.dr-
Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the
origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis.
Circulation =
Jo
F. dr
=
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY