For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 336. [T] Use a computer algebraic system (CAS) and Stokes’ theorem to approximate line integral ∫ c ( y d x + z d y + x d z ) , when C is the intersection of plane x + y = 2 and surface x 2 + y 2 + z 2 = 2 ( x + y ) , traversed counterclockwise viewed from the origin.
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 336. [T] Use a computer algebraic system (CAS) and Stokes’ theorem to approximate line integral ∫ c ( y d x + z d y + x d z ) , when C is the intersection of plane x + y = 2 and surface x 2 + y 2 + z 2 = 2 ( x + y ) , traversed counterclockwise viewed from the origin.
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
336. [T] Use a computer algebraic system (CAS) and Stokes’ theorem to approximate line integral
∫
c
(
y
d
x
+
z
d
y
+
x
d
z
)
, when C is the intersection of plane
x
+
y
=
2
and surface
x
2
+
y
2
+
z
2
=
2
(
x
+
y
)
, traversed counterclockwise viewed from the origin.
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.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.