Scalar line integrals in ℝ 3 Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. 26. ∫ C ( x + y + 2 z ) d s ; C is the circle r ( t ) = 〈 1 , 3 cos t , 3 sin t 〉 , for 0 ≤ t ≤ 2 π .
Scalar line integrals in ℝ 3 Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. 26. ∫ C ( x + y + 2 z ) d s ; C is the circle r ( t ) = 〈 1 , 3 cos t , 3 sin t 〉 , for 0 ≤ t ≤ 2 π .
Scalar line integrals in
ℝ
3
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.
26.
∫
C
(
x
+
y
+
2
z
)
d
s
;
C is the circle
r
(
t
)
=
〈
1
,
3
cos
t
,
3
sin
t
〉
, for 0 ≤ t ≤ 2π.
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.
2ni
2n+i
1
(b) /
(c) /
(d) /
(iz – 1)³ dz.
3. Evaluate the integrals: (a)
sinh z dz,
cos 3z dz,
e*z dz,
-
T-i
23 + 3
4. Evaluate the integral P 2 + 3z – 10
dz, where C is the circle (a) |z + 3| = 3, (b) |2| = 3, (c) |z| = 7.
dz
5. Evaluate the integral
where C is the circle (a) |z| = 1, (b) |z+ 3| = 2, (c) |z – 3| = 2.
23(z – 4)'
C
Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.
$(5)
(5x+ sinh y)dy - (3y² + arctan x²) dx, where C is the boundary of the square with vertices (1, 3), (2, 3), (2, 4), and (1,4).
false
(Type an exact answer.)
(5x + sinh yldy – (3y® + arctan x
an x²) dx =
dx =
...
Evaluate
C
F · dr
using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results.
−sin(x) dx + z dy + y dz
C
C: smooth curve from (0, 0, 0) to
?
2
, 3, 5
Please Explain each step. I am getting confused.
Chapter 17 Solutions
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Calculus, Single Variable: Early Transcendentals (3rd Edition)
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