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Mathematics
Problem
A solid has base on
0
≤
x
≤
L
0\le x\le L
0
≤
x
≤
L
. At each
x
x
x
the cross section perpendicular to the
x
x
x
-axis is an equilateral triangle whose side length is
e
−
x
/
2
e^{-x/2}
e
−
x
/2
. If the volume of the solid is
3
8
\dfrac{\sqrt{3}}{8}
8
3
cubic units, what is the value of
L
L
L
? a)
ln
(
3
2
)
\ln\left(\dfrac{3}{2}\right)
ln
(
2
3
)
b)
1
2
\dfrac{1}{2}
2
1
c)
ln
2
\ln 2
ln
2
d)
ln
(
4
3
)
\ln\left(\dfrac{4}{3}\right)
ln
(
3
4
)
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