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Mathematics
Mathematics
Problem
Define
g
(
x
)
=
{
x
2
,
0
≤
x
<
2
,
4
−
x
,
x
≥
2
,
g(x)=\begin{cases}x^{2}, & 0\le x<2,\\ 4-x, & x\ge 2,\end{cases}
g
(
x
)
=
{
x
2
,
4
−
x
,
0
≤
x
<
2
,
x
≥
2
,
and let
R
(
x
)
=
∫
1
g
(
x
)
1
+
t
6
d
t
.
R(x)=\int_{1}^{g(x)} \sqrt{1+t^{6}}\,dt.
R
(
x
)
=
∫
1
g
(
x
)
1
+
t
6
d
t
.
Determine
R
′
(
3
)
R'(3)
R
′
(
3
)
.
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