Find the length of the arc of the curve y = x(2-x) as x varies from 0 to 2.
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Answer:
I used WolframAlpha
s
=
∫
1
0
√
1
+
sinh
2
(
x
)
d
x
≈
1.1752
Explanation:
From the reference on Arc Length we write the equation:
s
=
∫
b
a
√
1
+
(
d
y
d
x
)
2
d
x
Given:
a
=
0
,
b
=
1
,
and
y
=
cosh
(
x
)
We know that
d
y
d
x
=
sinh
(
x
)
The arc length integral is:
s
=
∫
1
0
√
1
+
sinh
2
(
x
)
d
x
≈
1.1752
Step-by-step explanation:
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