Change the following integral to polar coordinates and evaluate: 4-x² [2² 0 x² + y² dy dx Sketo

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Change the following integral to polar coordinates and evaluate:
√4-x²
[²₁²²²22² + y² dy da
-2 JO
X
Sketc
Transcribed Image Text:Change the following integral to polar coordinates and evaluate: √4-x² [²₁²²²22² + y² dy da -2 JO X Sketc
Expert Solution
Step 1

To convert Cartesian coordinates into polar coordinates we use the following transformation,

x=rcosθ , y=rsinθ 

So, r=x2+y2 and θ=tan-1yx and dydx=rdrdθ

 

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