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Mathematics
Problem
If the value of definite integral
∫
1
a
x
⋅
a
−
[
log
a
x
]
d
x
\int_{1}^{a} x \cdot a^{-[\log_a x]} dx
∫
1
a
x
⋅
a
−
[
l
o
g
a
x
]
d
x
, where
a
>
1
a > 1
a
>
1
and
[
x
]
[x]
[
x
]
denotes the greatest integer, is
e
−
1
2
\frac{e-1}{2}
2
e
−
1
, then the value of '
a
a
a
' equals to a.
e
\sqrt{e}
e
b.
e
e
e
c.
e
+
1
\sqrt{e+1}
e
+
1
d.
e
−
1
e-1
e
−
1
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