/16–y²/32–a²-y²4VI (z² + y² + z*)dzdædy into spherical coordinates.Convert2²+y²T/4•T/2• 4/2T pt cos pdpdodý-T/2 Jo•T/4п/24sin ødpdodø4/2ρ' sin φdρdθdφ* /47/2•T/4• T/2• 4/2pdpdodø-T/2 Jo4/2ρ' sin φαρdφ dθ•T/4•T/2• 27/3• 4/2T/2 JoT/3• T/2• 4/2pdpdodø

from the integral limits are as follows 0 ≤ x ≤ 16-y2 0 ≤ y ≤ 4 x2+y2 ≤ z ≤ 32-x2-y2

/16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2 T p* sin ødpdodø •7/4 •T/2 /2 ρ' sin φdρdθd -1/2 Jo • 7/4 • 7/2 p4v2

/16–y² /32–2²-y² n[L 2² + y* + z®)dzdzdy in nvert 1²+y² •1/2 4/2 -/2 Jo п/2 " T p* sin ódpdődý •4/2 T p* sin ødpdodø •7/4 •T/2 /2 ρ' sin φdρdθd -1/2 Jo • 7/4 • 7/2 p4v2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 34E

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Question

/16–y²
/32–a²-y²
4
V
I (z² + y² + z*)dzdædy into spherical coordinates.
Convert
2²+y²
T/4
•T/2
• 4/2
T pt cos pdpdodý
-T/2 Jo
•T/4
п/2
4
sin ødpdodø
4/2
ρ' sin φdρdθdφ
* /4
7/2
•T/4
• T/2
• 4/2
pdpdodø
-T/2 Jo
4/2
ρ' sin φαρdφ dθ
•T/4
•T/2
• 27/3
• 4/2
T/2 Jo
T/3
• T/2
• 4/2
pdpdodø

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