Find the mass of the solid B that lies in the first octant, above the cone z = 3x² + 3y2, and • below the sphere x² + y² + z² = 16, given that its density is Hints: 8(x, y, z)=√√x² + y². (i) Use spherical coordinates. (ii) The first octant in R³ consists of the set of all (x, y, z) such that x ≥ 0, y ≥ 0, and z ≥ 0. (iii) Observing that √3x2 + 3y2 √√√√x² + y² may help you describe the cone in spher- √x² + y² ical coordinates. (Recall that q = arctan Z (iv) The trigonometric identity sin² 9 cos(2p)) is useful if you have to inte- 2² (1 + cos(24)) is useful if you have to - 2 grate sin² p. Similarly, the identity cos² q = integrate cos² p.
Find the mass of the solid B that lies in the first octant, above the cone z = 3x² + 3y2, and • below the sphere x² + y² + z² = 16, given that its density is Hints: 8(x, y, z)=√√x² + y². (i) Use spherical coordinates. (ii) The first octant in R³ consists of the set of all (x, y, z) such that x ≥ 0, y ≥ 0, and z ≥ 0. (iii) Observing that √3x2 + 3y2 √√√√x² + y² may help you describe the cone in spher- √x² + y² ical coordinates. (Recall that q = arctan Z (iv) The trigonometric identity sin² 9 cos(2p)) is useful if you have to inte- 2² (1 + cos(24)) is useful if you have to - 2 grate sin² p. Similarly, the identity cos² q = integrate cos² p.
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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Transcribed Image Text:Find the mass of the solid B that lies
in the first octant,
above the cone z =
3x² + 3y², and
• below the sphere x² + y² + z² = 16,
given that its density is
Hints:
6(x, y, z)=√x² + y².
(i) Use spherical coordinates.
(ii) The first octant in R³ consists of the set of all (x, y, z) such that x ≥ 0, y ≥ 0, and
z ≥ 0.
(iii) Observing that √3x² + 3y² = √√3√√x² + y² may help you describe the cone in spher-
/x² + y²
ical coordinates. (Recall that q = arctan
Z
1
(iv) The trigonometric identity sin² ዋ =
grate sin² p. Similarly, the identity cos² q
integrate cos² 9.
(1 – cos(2p)) is useful if you have to inte-
=(1+ + cos(2p)) is useful if you have to
=
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