Question
Download Solution PDF Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
We are given the double integral over the positive quadrant of the circle
Region of Integration:
The circle
, ,
So, the limits become:
- y from 0 to 1
- for each y, x goes from 0 to √(1 - y2)
Calculation:
Take constants outside the inner integral:
Inner integral:
So the expression becomes:
Use substitution: Let
Change limits:
So the integral becomes:
Integrating:
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