I need your help in this problem dvUse spherical Coordinaresffto Computewhere W is the solid bounded by the spheresx'ty+z" =g ty tz?= 42.%3Dx² ty"tz

Answered: dv Use spherical Coordinares to compute…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

See similar textbooks

Related questions

Question

I need your help in this problem

dv
Use spherical Coordinares
ff
to Compute
where W is the solid bounded by the spheres
x'ty+z" =g ty tz?= 4
2.
%3D
x² ty"tz

Expert Solution

Step 1

Given

$I = \int \int \int_{w} \frac{d V}{\sqrt{x^{2} + y^{2} + z^{2}}} W h e r e W i s t h e s o l i d b o u n d e d b y t h e s p h e r e s x^{2} + y^{2} + z^{2} = 9 a n d x^{2} + y^{2} + z^{2} = 4 .$

Step 2

Now

$U s e t h e s p h e r i c a l c o o r d i n a t e s x = ρ \cos θ \sin ϕ y = ρ \sin θ \sin ϕ z = ρ \cos ϕ a n d x^{2} + y^{2} + z^{2} = {(ρ \cos θ \sin ϕ)}^{2} + {(ρ \sin θ \sin ϕ)}^{2} + {(ρ \cos ϕ)}^{2} x^{2} + y^{2} + z^{2} = ρ^{2} [{(\sin ϕ)}^{2} ({(\cos θ)}^{2} + {(\sin θ)}^{2}) + {(\cos ϕ)}^{2}] x^{2} + y^{2} + z^{2} = ρ^{2} [{(\sin ϕ)}^{2} (1) + {(\cos ϕ)}^{2}] x^{2} + y^{2} + z^{2} = ρ^{2} [1] \{i f w e k n o w \cos^{2} x + \sin^{2} x = 1\} t h e n w e h a v e x^{2} + y^{2} + z^{2} = ρ^{2} a n d g i v e n x^{2} + y^{2} + z^{2} = 9, x^{2} + y^{2} + z^{2} = 4 ρ^{2} = 9, ρ^{2} = 4 ρ = 3, ρ = 2 S o t h e l i m i t i s 2 \leq ρ \leq 3 0 \leq ϕ \leq π 0 \leq θ \leq 2 π$

Step by step

Solved in 3 steps

Knowledge Booster

$Research Ethics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions