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The region W is the cone shown below. The angle at the vertex is π/3, and the top is flat and at a height of 4√/3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry) (a) Cartesian:

The region W is the cone shown below. The angle at the vertex is π/3, and the top is flat and at a height of 4√/3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry) (a) Cartesian:

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 23E
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The region W is the cone shown below. The angle at the vertex is π/3, and the top is flat and at a height of 4√/3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian:
Transcribed Image Text:The region W is the cone shown below. The angle at the vertex is π/3, and the top is flat and at a height of 4√/3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian:
The angle at the vertex is π/3, and the top is flat and at a height of 4√3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = -4 C = -sqrt(16-x^2) e = -sqrt((x^2+y^2)/3) ob ed Volume = S S S 1 (b) Cylindrical: With a = 0 c = 0 e = 0 bed Volume = SS Ser 7 d = and f= = = b= 4 sqrt(16-x^2) (c) Spherical: With a = 0 c = 0 e = 0 b ed Volume = S S S rho^2sin(phi) -4/sqrt(3) dz b = 2*pi 4sqrt(3) and f = 4 = pi dr , d = pi/3 , and f = (4/sqrt3)cos(phi) d rho dy dz d phi d x d theta d theta
Transcribed Image Text:The angle at the vertex is π/3, and the top is flat and at a height of 4√3. Write the limits of integration for Sw dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = -4 C = -sqrt(16-x^2) e = -sqrt((x^2+y^2)/3) ob ed Volume = S S S 1 (b) Cylindrical: With a = 0 c = 0 e = 0 bed Volume = SS Ser 7 d = and f= = = b= 4 sqrt(16-x^2) (c) Spherical: With a = 0 c = 0 e = 0 b ed Volume = S S S rho^2sin(phi) -4/sqrt(3) dz b = 2*pi 4sqrt(3) and f = 4 = pi dr , d = pi/3 , and f = (4/sqrt3)cos(phi) d rho dy dz d phi d x d theta d theta
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