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
]
Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C
is the curve following the outline for the triangle from (1,0,0) to (0,1,0) to (0, 0, 1)
and back to (1,0,0).
b) Find the directional derivative (D.) of the function at P in the direction of PQ
f (r, y) = sin 2x cos y, P(T, 0), Q()
Find the parametric equations of the tangent line LT to the curve
C:r(t) = 2 cos(t)i + sin(t)j + 2tk
at the point (-2, 0, 27)
Chapter 16 Solutions
Bundle: Calculus, 8th + Enhanced WebAssign - Start Smart Guide for Students + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Multi-Term
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