Find the length of the curve 3 2x y = + from (0, 3) to (2, 4).
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Answered by
0
Answer:
S
=
1
6
(
(
37
)
3
2
−
1
)
Explanation:
Given equation is
f
(
x
)
=
2
x
3
2
.
We are given the task to find the length of the curve of the given equation in the interval
(
0
,
4
)
.
The equation to find length of the curve is
S
=
∫
4
0
√
1
+
f
'
(
x
)
2
d
x
So, the derivative of the given equation will be
f
'
(
x
)
=
2
d
d
x
(
x
3
2
)
=
2
⋅
3
2
⋅
x
3
2
−
1
=
3
⋅
x
1
2
So substituting for
f
'
(
x
)
,
S
=
∫
4
0
√
1
+
9
x
d
x
Taking
9
x
=
t
⇒
d
x
=
d
t
9
and that at
x
=
0
⇒
t
=
0
and
x
=
4
⇒
t
=
36
So the given integral becomes
S
=
1
9
∫
36
0
√
1
+
t
d
t
So,
S
=
3
1
2
⋅
1
9
3
(
1
+
t
)
3
2
∣
∣
∣
∣
36
0
Applying limits and totalling, I get the above answer.
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