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

## Question:

(a) We define the improper integral (over the entire plane R^{2}d)where D_{a} is the disk with radius a and center the origin. Show that

(b) An equivalent definition of the improper integral in part (a) iswhere S_{a} 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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## Step by Step Answer:

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**Question Details**

Chapter #

**15**- Multiple IntegralsSection: Exercises 15-3

Problem: 40

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