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Putnam
1942 Putnam
B5
B5
Part of
1942 Putnam
Problems
(1)
Putnam 1942 B5
Source: Putnam 1942
3/1/2022
Sketch the curve
y
=
x
1
+
x
6
(
sin
x
)
2
,
y= \frac{x}{1+x^6 (\sin x)^{2}},
y
=
1
+
x
6
(
sin
x
)
2
x
,
and show that
∫
0
∞
x
1
+
x
6
(
sin
x
)
2
d
x
\int_{0}^{\infty} \frac{x}{1+x^6 (\sin x)^{2}}\; dx
∫
0
∞
1
+
x
6
(
sin
x
)
2
x
d
x
exists.
Putnam
trigonometry
integration