Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer algebra system to evaluate ∫ c F · d r . F ( x , y , z ) = x 2 z i + 6 y j + y z 2 k C : r ( t ) = t i + t 2 j + ln t k , 1 ≤ t ≤ 3
Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer algebra system to evaluate ∫ c F · d r . F ( x , y , z ) = x 2 z i + 6 y j + y z 2 k C : r ( t ) = t i + t 2 j + ln t k , 1 ≤ t ≤ 3
Solution Summary: The author explains how to calculate the line integral displaystyle 'underset' Cint's F.dr over the curve.
Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer algebra system to evaluate
∫
c
F
·
d
r
.
F(x, y, z) =
x
2
z
i
+
6
y
j
+
y
z
2
k
C
:
r
(
t
)
=
t
i
+
t
2
j
+
ln
t
k
,
1
≤
t
≤
3
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.
Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
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