(a) We define the improper integral (over the entire plane R 2 d) where D a is the disk with...


(a) We define the improper integral (over the entire plane R2d)le-42+y?) dA -(x²+y²) -Se-ta?4y?, R2 -(x²+y²) dy dx - 00 -00 -(x²+y²) = lim dA Da where Da is the disk with radius a and center the origin. Show that

e-(x²+y²) dA = T o,

(b) An equivalent definition of the improper integral in part (a) iswhere Sa is the square with vertices (±a, ±a). Use this to show that

(c) Deduce that

(d) By making the change of variable t = √2 x, show that

(This is a fundamental result for probability and statistics.)

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Question Details
Chapter # 15- Multiple Integrals
Section: Exercises 15-3
Problem: 40
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Question Posted: April 10, 2019 10:17:22