We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with vertices R, R+ it, -R+it, -R. (a) What is the value of fe-²/² dz? (b) Write the complex line integral in (a) as a sum of four integrals in a real parameter, i.e., four integrals of the form fo... dt. (c) Letting R→ ∞, and using the fact that e-²/2 dx = 1, show that √ 100 -1²/2e-itz dre-t²/2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3.
We will try to compute the real
integrale-2²/²e-it dr.
Let R> 0 and let y be the rectangle with vertices R, R+ it, -R+ it, -R.
(a) What is the value of f, e-*²/2 dz?
(b) Write the complex line integral in (a) as a sum of four integrals in a real parameter, i.e., four
integrals of the form fo... dt.
(c) Letting R→ ∞, and using the fact that fe-²/2 dx = 1, show that
2/² €
√ZT 100
√2π
dr
e-t²/2
= e
Transcribed Image Text:3. We will try to compute the real integrale-2²/²e-it dr. Let R> 0 and let y be the rectangle with vertices R, R+ it, -R+ it, -R. (a) What is the value of f, e-*²/2 dz? (b) Write the complex line integral in (a) as a sum of four integrals in a real parameter, i.e., four integrals of the form fo... dt. (c) Letting R→ ∞, and using the fact that fe-²/2 dx = 1, show that 2/² € √ZT 100 √2π dr e-t²/2 = e
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