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Putnam
1993 Putnam
A1
A1
Part of
1993 Putnam
Problems
(1)
Putnam 1993 A1
Source: 1993 Putnam
10/26/2020
Let
O
O
O
be the origin.
y
=
c
y = c
y
=
c
intersects the curve
y
=
2
x
ā
3
x
3
y = 2x - 3x^3
y
=
2
x
ā
3
x
3
at
P
P
P
and
Q
Q
Q
in the first quadrant and cuts the y-axis at
R
R
R
. Find
c
c
c
so that the region
O
P
R
OPR
OPR
bounded by the y-axis, the line
y
=
c
y = c
y
=
c
and the curve has the same area as the region between
P
P
P
and
Q
Q
Q
under the curve and above the line
y
=
c
y = c
y
=
c
.
Putnam