(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)where Da is the disk with radius a and center the origin. Show that
(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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