7. Evaluate the surface integral: (a) f(x,y,z) = x + y+ z where S is the parallelogram with parametric equations x = u + v, y = u - v and z = 1+ u + 2v where 0 < u < 1,0 < v < 2. (b) f(x,y, z) = y²z² and S is the part of the cone y = vx² + z² that lies between the planes y = 1 and y = 4.
7. Evaluate the surface integral: (a) f(x,y,z) = x + y+ z where S is the parallelogram with parametric equations x = u + v, y = u - v and z = 1+ u + 2v where 0 < u < 1,0 < v < 2. (b) f(x,y, z) = y²z² and S is the part of the cone y = vx² + z² that lies between the planes y = 1 and y = 4.
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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Please need solution for number 7 and 8
Transcribed Image Text:7. Evaluate the surface integral:
(a) f(x, y, z) = x + y + z where S is the parallelogram with parametric equations
x = u + v, y = u – v and z = 1 + u + 2v where 0 <u < 1,0< v < 2.
(b) f(x,y, z) = y²z² and S is the part of the cone y = vx² + z² that lies between
the planes y = 1 and y = 4.
8. Evaluate the surface integral Sf. F dS for the given vector field F and the oriented
surface S.
(a) F(x,y,z) = xyi + yzj + zxk, S is the part of the paraboloid z = 4 – x² – y?
that lies above the square 0 <x < 1,0 < y< 1, and has upward orientation.
(b) F(x,y,z) = yj – zk, S consists of the paraboloid y = x2 + z², 0< y< 1, and
the disk x? + z2 < 1, y = 1.
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