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If the value of definite integral
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
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 (1)
e
\sqrt{e}
e
(2)
e
e
e
(3)
e
+
1
\sqrt{e+1}
e
+
1
(4)
e
−
1
e-1
e
−
1
Related theory
Special Functions
Properties of Definite Integrals
Accumulation Concepts
Integrals
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