5. (a) Evaluate the surface integral || ²: y²2² dS where o is part of the cone z = Vr + y that lies between the planes z 1 and 2 = 2. (b) Use Gauss' Theorem to evaluate //F-nds, where F(r, y, 2) = ri+y'j+z*k and o is the closed surface of a hemisphere z = V16 – 1² – y² and the ry-plane. (c) Use Stokes' Theorem to evaluate fF. dr where F(z, y, 2) = 2yi + zj + rk and C is the boundary of the surface in the first octant obtained from the intersection of the plane 3r +y+3z = 3 with the coordinate planes, with the orien- tation counterclockwise looking from above.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Answer all a,b,and c
5. (a) Evaluate the surface integral // y²z².
y22 dS where o is part of the
cone z = Vr + y that lies between the planes z = 1 and 2 2.
(b) Use Gauss' Theorem to evaluate
F-no
where F(z, y, 2) = r’i+ y*j+ z*k and o is the closed surface of a
hemisphere z = V16 – r² – y? and the ry-plane.
(c) Use Stokes' Theorem to evaluate
F. dr
where F(r, y, 2) = 2yi + zj + rk and C is the boundary of the
surface in the first octant obtained from the intersection of the
plane 3r + y+3z = 3 with the coordinate planes, with the orien-
tation counterclockwise looking from above.
Transcribed Image Text:5. (a) Evaluate the surface integral // y²z². y22 dS where o is part of the cone z = Vr + y that lies between the planes z = 1 and 2 2. (b) Use Gauss' Theorem to evaluate F-no where F(z, y, 2) = r’i+ y*j+ z*k and o is the closed surface of a hemisphere z = V16 – r² – y? and the ry-plane. (c) Use Stokes' Theorem to evaluate F. dr where F(r, y, 2) = 2yi + zj + rk and C is the boundary of the surface in the first octant obtained from the intersection of the plane 3r + y+3z = 3 with the coordinate planes, with the orien- tation counterclockwise looking from above.
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