Consider the surface 2? - y + z? + 2az = 9. (a) Parametrise the surface in terms of two scalar parameters u and v. (b) Calculate the normal vector N(u, v) and state an integral to describe the surface area of that part of the surface for which your parameters lie in the region 2 of the uv-plane. (c) Give a double integral which would yield the surface area of that part of the surface where y <0 and 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the surface
2? - y + z? + 2az = 9.
(a) Parametrise the surface in terms of two scalar parameters u and v.
(b) Calculate the normal vector N(u, v) and state an integral to describe the surface area of that part of the surface
for which your parameters lie in the region 2 of the uv-plane.
(c) Give a double integral which would yield the surface area of that part of the surface where y < 0 and
(d) Evaluate your integral from part (c).
You may use the result
1
(2as/(1+2a°s*) + v2 sinh ' (as/2)
4a
Transcribed Image Text:Consider the surface 2? - y + z? + 2az = 9. (a) Parametrise the surface in terms of two scalar parameters u and v. (b) Calculate the normal vector N(u, v) and state an integral to describe the surface area of that part of the surface for which your parameters lie in the region 2 of the uv-plane. (c) Give a double integral which would yield the surface area of that part of the surface where y < 0 and (d) Evaluate your integral from part (c). You may use the result 1 (2as/(1+2a°s*) + v2 sinh ' (as/2) 4a
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