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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Probability

The value of the integral

I = e x 2 2 d x

Is required in the normal probability density function.

a) Use polar coordinates to evaluate the improper integral.

I 2 = ( e x 2 2 d x ) ( e y 2 2 d y ) I 2 = e ( x 2 + y 2 ) 2 d A

b) Use the result of part (a) to determine I.

(a)

To determine

To calculate: The value of the integral I=ex22dx by converting to polar coordinates.

Explanation

Given:

I=ex22dx

Calculation:

First convert the integral into polar coordinates by substituting:

x=rcosθy=rsinθdxdy=rdrdθ

The corresponding limits in polar coordinates will be:

0θπ20r

Writing the double integral in polar coordinates:

I=ex22dxey22dy

I2=

(b)

To determine

To Calculate: The value of the integral by using results in a).

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Chapter 14 Solutions

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