Scalar line integrals in ℝ 3 Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. 25. ∫ C ( x + y + z ) d s ; C is the circle r ( t ) = 〈 2 cos t , 0 2 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. 25. ∫ C ( x + y + z ) d s ; C is the circle r ( t ) = 〈 2 cos t , 0 2 sin t 〉 , for 0 ≤ t ≤ 2 π .
Solution Summary: The author explains how the line integral displaystyleundersetCint is converted into an ordinary integral and then to evaluate the value.
Scalar line integrals in
ℝ
3
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.
25.
∫
C
(
x
+
y
+
z
)
d
s
;
C is the circle
r
(
t
)
=
〈
2
cos
t
,
0
2
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.
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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 =
...
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