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: With a 0 b= 4sqrt3 C=-12 d = 12 e-sqrt(z^2-x^2) Volume = Så Sª² Se² 1 (b) Cylindrical: With a 0 c = 0 b= 2pi d=4sqrt3 and f sqrt(z^2-x^2) d d x dz y e=0 and f= sqrt3z Volume = So Sd S r dr dz d theta (c) Spherical: With a 0 b= 2pi C=0 d pi/6 e=0 ' and f = 8 Volume = Sº Sª² Se² rho^2sin(phi) d rho d lamda 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: With a 0 b= 4sqrt3 C=-12 d = 12 e-sqrt(z^2-x^2) Volume = Så Sª² Se² 1 (b) Cylindrical: With a 0 c = 0 b= 2pi d=4sqrt3 and f sqrt(z^2-x^2) d d x dz y e=0 and f= sqrt3z Volume = So Sd S r dr dz d theta (c) Spherical: With a 0 b= 2pi C=0 d pi/6 e=0 ' and f = 8 Volume = Sº Sª² Se² rho^2sin(phi) d rho d lamda d theta

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 21E

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