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1. Evaluate the following surface integrals: (x + y) dS, o : part of the surface 2x + 3y + z = 6 in the first octant. || Vx² + y² + z² dS, o : the part of the surface of the cone z = Vx2 + y² from z = 0 to z = 1. (b) o : the surface of the cuboid in the first octant bounded by x = 1, y = 1 and z = 1. (c) dS, (d) (x² o : the surface of the sphere x² + y² + z² = 4.

1. Evaluate the following surface integrals: (x + y) dS, o : part of the surface 2x + 3y + z = 6 in the first octant. || Vx² + y² + z² dS, o : the part of the surface of the cone z = Vx2 + y² from z = 0 to z = 1. (b) o : the surface of the cuboid in the first octant bounded by x = 1, y = 1 and z = 1. (c) dS, (d) (x² o : the surface of the sphere x² + y² + z² = 4.

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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Surface integrals

1. Evaluate the following surface integrals: (x + y)d. 0 : part of the surface 2x + 3y + z = 6 in the first octant. (a) (b) || Vx2 + y² + z² dS, o : the part of the surface of the cone z = Vx² + y² from z = 0 to z = 1. o : the surface of the cuboid in the first octant bounded by x = 1, y = 1 and z = 1. (c) dS, (d) || (x² + y²) dS, o : the surface of the sphere x² + y² + z² = 4.
Transcribed Image Text:1. Evaluate the following surface integrals: (x + y)d. 0 : part of the surface 2x + 3y + z = 6 in the first octant. (a) (b) || Vx2 + y² + z² dS, o : the part of the surface of the cone z = Vx² + y² from z = 0 to z = 1. o : the surface of the cuboid in the first octant bounded by x = 1, y = 1 and z = 1. (c) dS, (d) || (x² + y²) dS, o : the surface of the sphere x² + y² + z² = 4.
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