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10
2016 Calculus #10
2016 Calculus #10
Source:
August 8, 2022
2016
Calculus Test
Problem Statement
Using the fact that
∑
n
=
1
∞
1
n
2
=
π
2
6
,
\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6},
n
=
1
∑
∞
n
2
1
=
6
π
2
,
compute
∫
0
1
(
ln
x
)
ln
(
1
−
x
)
d
x
.
\int_0^1(\ln x)\ln(1-x)dx.
∫
0
1
(
ln
x
)
ln
(
1
−
x
)
d
x
.
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