Evaluate ∫ C ( y + sin x ) d x + ( z 2 + cos y ) d y + x 3 d z where C is the curve r ( t ) = 〈 sin t , cos t , sin 2 t 〉 , 0 ≤ t ≤ 2 π .[ Hint: Observe that C lies on the surface z = 2 x y ]
Evaluate ∫ C ( y + sin x ) d x + ( z 2 + cos y ) d y + x 3 d z where C is the curve r ( t ) = 〈 sin t , cos t , sin 2 t 〉 , 0 ≤ t ≤ 2 π .[ Hint: Observe that C lies on the surface z = 2 x y ]
Solution Summary: The author explains Stokes' Theorem: Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed, piece-wise, smooth boundary curve C
Evaluate
∫
C
(
y
+
sin
x
)
d
x
+
(
z
2
+
cos
y
)
d
y
+
x
3
d
z
where C is the curve
r
(
t
)
=
〈
sin
t
,
cos
t
,
sin
2
t
〉
,
0
≤
t
≤
2
π
.[Hint:Observe that C lies on the surface
z
=
2
x
y
]
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