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.
Hi, Im stuck on how to prove this following problem relating to vector fields, thank you!
Use the equation giving the flux of the vector field across the curve to calculate the flux of
x + 1
y
lã
(x + 1)² + y²' (x + 1)² + y²
F(x, y) =
across C, the segment 7 ≤ y ≤ 9 along the y-axis, oriented upwards.
(Use symbolic notation and fractions where needed.)
I
F. dr =
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