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19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown.

19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11, p = 1, 0 = φ < π/6, 0 = 0 < π 12. 1 < p = 2, 13. 2 < p = 4, 14. p ≤ 2, p≤ csc X 15. A solid lies above the cone z = √√√x² + y² and below the sphere x² + y² + z² = z. Write a description of the solid in terms of inequalities involving spherical coordinates. 16. (a) Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have posi- tioned the coordinate system that you have chosen. (b) Suppose the ball is cut in half. Write inequalities that describe one of the halves. 17-18 Sketch the solid whose volume is given by the integral and evaluate the integral. 17. π/2 < φ = π 0 = φ = π/3, 0 = 0 < π gag on i T/6 3 21 0 2 ²p² sin & dp de dó π/4 27 seco 2 18. S/2 p² sin & dp dº do 19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown. 19. 3 ΖΑ ZAU mom stave ruba y sdg 20. XX 2 ZA 21-34 Use spherical coordinates. 21. Evaluate fff (x² + y² + z²)²dV, where B is the ball with center the origin and radius 5. S the cones. 28. Find the a its center. 29. (a) Find t Ф= 1 (b) Find t 30. Find the v x² + y² + z = √x² 31. (a) Find t stant c (b) Find t 32. Let H be a point is pr (a) Find t (b) Find t (c) Find t 33. (a) Find t radius (b) Find t diame 34. Find the m radius a if distance fr 35-40 Use cy more appropria 35. Find the v cone z = 36. Find the v radius a by angle of T 37. A solid cy height h. (a) Find t (b) Find th of its
Transcribed Image Text:11, p = 1, 0 = φ < π/6, 0 = 0 < π 12. 1 < p = 2, 13. 2 < p = 4, 14. p ≤ 2, p≤ csc X 15. A solid lies above the cone z = √√√x² + y² and below the sphere x² + y² + z² = z. Write a description of the solid in terms of inequalities involving spherical coordinates. 16. (a) Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have posi- tioned the coordinate system that you have chosen. (b) Suppose the ball is cut in half. Write inequalities that describe one of the halves. 17-18 Sketch the solid whose volume is given by the integral and evaluate the integral. 17. π/2 < φ = π 0 = φ = π/3, 0 = 0 < π gag on i T/6 3 21 0 2 ²p² sin & dp de dó π/4 27 seco 2 18. S/2 p² sin & dp dº do 19-20 Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over the solid shown. 19. 3 ΖΑ ZAU mom stave ruba y sdg 20. XX 2 ZA 21-34 Use spherical coordinates. 21. Evaluate fff (x² + y² + z²)²dV, where B is the ball with center the origin and radius 5. S the cones. 28. Find the a its center. 29. (a) Find t Ф= 1 (b) Find t 30. Find the v x² + y² + z = √x² 31. (a) Find t stant c (b) Find t 32. Let H be a point is pr (a) Find t (b) Find t (c) Find t 33. (a) Find t radius (b) Find t diame 34. Find the m radius a if distance fr 35-40 Use cy more appropria 35. Find the v cone z = 36. Find the v radius a by angle of T 37. A solid cy height h. (a) Find t (b) Find th of its
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