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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(3(x^2+y^2)) Volume = S SS1 (b) Cylindrical: With a = 0 c = 0 e = 0 d Volume = S SS Så r (c) Spherical: With a = 0 c = 0 b= 4 d = sqrt(16-x^2) and f = 4sqrt(3) dz b=2"pi d= 4sqrt(3) and f = -4sqrt3 b = 2pi e = 0 ·b ed Volume = SSS rho^2sin(phi) dr d = pi/6 and f= (4*sqrt3)/cos(phi) d rho dy dz d phi d x d theta d theta

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(3(x^2+y^2)) Volume = S SS1 (b) Cylindrical: With a = 0 c = 0 e = 0 d Volume = S SS Så r (c) Spherical: With a = 0 c = 0 b= 4 d = sqrt(16-x^2) and f = 4sqrt(3) dz b=2"pi d= 4sqrt(3) and f = -4sqrt3 b = 2pi e = 0 ·b ed Volume = SSS rho^2sin(phi) dr d = pi/6 and f= (4*sqrt3)/cos(phi) d rho dy dz d phi d x d theta d theta

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 angle at the vertex is +/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(3(x^2+y^2)) Volume = = Så Så Sé 1 (b) Cylindrical: With a = 0 c = 0 e = 0 Volume = S S Ser b = (c) Spherical: With a = 0 C = 0 e = 0 Volume = f Srho^2sin(phi) 4 d sqrt(16-x^2) and f = 4sqrt(3) dz b = 2*pi d = 4sqrt(3) and f = -4sqrt3 b= 2pi dr d pi/6 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 +/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(3(x^2+y^2)) Volume = = Så Så Sé 1 (b) Cylindrical: With a = 0 c = 0 e = 0 Volume = S S Ser b = (c) Spherical: With a = 0 C = 0 e = 0 Volume = f Srho^2sin(phi) 4 d sqrt(16-x^2) and f = 4sqrt(3) dz b = 2*pi d = 4sqrt(3) and f = -4sqrt3 b= 2pi dr d pi/6 and f= (4 *sqrt3)/cos(phi) d rho dy dz d phi d x d theta d theta
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:
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