Evaluating line integrals Evaluate the line integral ∫ C F ⋅ d r for the following vector fields F and curves C in two ways. a. By parameterizing C b. By using the Fundamental Theorem for line integrals, if possible 25. F = ∇ ( x y z ) ; C : r ( t ) = 〈 cos t , sin t , t / π 〉 , for 0 ≤ t ≤ π
Evaluating line integrals Evaluate the line integral ∫ C F ⋅ d r for the following vector fields F and curves C in two ways. a. By parameterizing C b. By using the Fundamental Theorem for line integrals, if possible 25. F = ∇ ( x y z ) ; C : r ( t ) = 〈 cos t , sin t , t / π 〉 , for 0 ≤ t ≤ π
Solution Summary: The author evaluates the integral of the function F=Delta(xyz) by using the parametric description of C.
Evaluating line integralsEvaluate the line integral
∫
C
F
⋅
d
r
for the following vector fieldsFand curves C in two ways.
a. By parameterizing C
b. By using the Fundamental Theorem for line integrals, if possible
25.
F
=
∇
(
x
y
z
)
;
C
:
r
(
t
)
=
〈
cos
t
,
sin
t
,
t
/
π
〉
,
for 0 ≤ t ≤ π
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Let
r(t)=cos 2t i +sin 2t j + t k
be a vector function. Which of the followings are true for this function?
I. Tangent vector is constant at any point.
II. Length of tangent vector at any point is constant.
II. Tangent vector is (0,2,1) at the point (1,0,0).
IV. Curvature at a point (a, b,
4а+b
c) is
50
V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by
V5dt
O a. II, II, IV
Ob. II, II, V
O C. I, II, V
Od.I, II, IV
I need help with this problem becuase I don't know
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