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Mathematics
Problem
Which differential element must be used to express the exact arc length
L
L
L
of a differentiable function
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
on the interval
[
a
,
b
]
[a,b]
[
a
,
b
]
? a)
1
+
(
d
y
d
x
)
2
d
x
\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}\,dx
1
+
(
d
x
d
y
)
2
d
x
b)
(
d
y
d
x
)
2
d
x
\sqrt{\left(\dfrac{dy}{dx}\right)^2}\,dx
(
d
x
d
y
)
2
d
x
c)
(
1
+
(
d
y
d
x
)
2
)
d
x
(1+\left(\dfrac{dy}{dx}\right)^2)dx
(
1
+
(
d
x
d
y
)
2
)
d
x
d)
1
+
(
d
x
d
y
)
2
d
x
\sqrt{1+\left(\dfrac{dx}{dy}\right)^2}\,dx
1
+
(
d
y
d
x
)
2
d
x
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