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Arnold's Trivium
1991 Arnold's Trivium
52
Problem 52
Problem 52
Source:
July 1, 2010
calculus
integration
function
Problem Statement
Calculate the first term of the asymptotic expression as
k
→
∞
k\to\infty
k
→
∞
of the integral
∫
−
∞
+
∞
e
i
k
x
1
+
x
2
n
d
x
\int_{-\infty}^{+\infty}\frac{e^{ikx}}{\sqrt{1+x^{2n}}}dx
∫
−
∞
+
∞
1
+
x
2
n
e
ik
x
d
x
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