Use a CAS to evaluate the line integrals along the given curves. a ∫ C x 7 y 3 d s C : x = cos 3 t , y = sin 3 t ( 0 ≤ t ≤ π / 2 ) b ∫ C x 5 z d x + 7 y d y + y 2 z d z C : r ( t ) = t i + t 2 j + ln t k ( 1 ≤ t ≤ e )
Use a CAS to evaluate the line integrals along the given curves. a ∫ C x 7 y 3 d s C : x = cos 3 t , y = sin 3 t ( 0 ≤ t ≤ π / 2 ) b ∫ C x 5 z d x + 7 y d y + y 2 z d z C : r ( t ) = t i + t 2 j + ln t k ( 1 ≤ t ≤ e )
Use a CAS to evaluate the line integrals along the given curves.
a
∫
C
x
7
y
3
d
s
C
:
x
=
cos
3
t
,
y
=
sin
3
t
(
0
≤
t
≤
π
/
2
)
b
∫
C
x
5
z
d
x
+
7
y
d
y
+
y
2
z
d
z
C
:
r
(
t
)
=
t
i
+
t
2
j
+
ln
t
k
(
1
≤
t
≤
e
)
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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