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Mathematics
Problem
Let
g
g
g
be an even, differentiable function on
[
−
3
,
3
]
[-3,3]
[
−
3
,
3
]
. Which of the following expressions gives the length of the graph of
y
=
g
(
x
)
y=g(x)
y
=
g
(
x
)
on
[
−
3
,
3
]
[-3,3]
[
−
3
,
3
]
? a)
∫
−
3
3
1
+
(
g
(
x
)
)
2
d
x
\displaystyle\int_{-3}^{3}\sqrt{1+\bigl(g(x)\bigr)^{2}}\,dx
∫
−
3
3
1
+
(
g
(
x
)
)
2
d
x
b)
2
∫
0
3
∣
g
′
(
x
)
∣
d
x
\displaystyle 2\int_{0}^{3}\lvert g'(x)\rvert\,dx
2
∫
0
3
∣
g
′
(
x
)∣
d
x
c)
2
∫
0
3
1
+
(
g
′
(
x
)
)
2
d
x
\displaystyle 2\int_{0}^{3}\sqrt{1+\bigl(g'(x)\bigr)^{2}}\,dx
2
∫
0
3
1
+
(
g
′
(
x
)
)
2
d
x
d)
∫
0
3
1
+
(
g
′
(
x
)
)
2
d
x
\displaystyle\int_{0}^{3}\sqrt{1+\bigl(g'(x)\bigr)^{2}}\,dx
∫
0
3
1
+
(
g
′
(
x
)
)
2
d
x
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