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Mathematics
Mathematics
Problem
On the interval
[
−
6
,
6
]
[-\sqrt{6},\,\sqrt{6}]
[
−
6
,
6
]
, the curves
f
(
x
)
=
x
4
−
6
x
2
+
8
f(x)=x^{4}-6x^{2}+8
f
(
x
)
=
x
4
−
6
x
2
+
8
and
g
(
x
)
=
2
x
2
−
4
g(x)=2x^{2}-4
g
(
x
)
=
2
x
2
−
4
enclose several subregions. Compute the total area of all these enclosed regions. a)
224
15
2
−
32
5
6
\displaystyle \frac{224}{15}\sqrt{2}-\frac{32}{5}\sqrt{6}
15
224
2
−
5
32
6
b)
448
15
2
+
32
5
6
\displaystyle \frac{448}{15}\sqrt{2}+\frac{32}{5}\sqrt{6}
15
448
2
+
5
32
6
c)
448
15
2
−
32
5
6
\displaystyle \frac{448}{15}\sqrt{2}-\frac{32}{5}\sqrt{6}
15
448
2
−
5
32
6
d)
256
15
2
−
16
5
6
\displaystyle \frac{256}{15}\sqrt{2}-\frac{16}{5}\sqrt{6}
15
256
2
−
5
16
6
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