. The ellipsoid++= 1 can be parametrized using ellipsoidal coordinates x=asino cose, y=bsino sine, z=ccos, for 0≤0≤2 and 0 ≤ ≤. Show that the surface area S of the ellipsoid is S = "²" sino√/a²b² cos² + c²(a² sin²0 + b² cos²0) sin² $ de d$ . (Note: The above double integral can not be evaluated by elementary means. For specific values of a, b and c it can be evaluated using numerical methods. An alternative is to express the surface area in terms of elliptic integrals.5)
. The ellipsoid++= 1 can be parametrized using ellipsoidal coordinates x=asino cose, y=bsino sine, z=ccos, for 0≤0≤2 and 0 ≤ ≤. Show that the surface area S of the ellipsoid is S = "²" sino√/a²b² cos² + c²(a² sin²0 + b² cos²0) sin² $ de d$ . (Note: The above double integral can not be evaluated by elementary means. For specific values of a, b and c it can be evaluated using numerical methods. An alternative is to express the surface area in terms of elliptic integrals.5)
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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10. The ellipsoid++=1 can be parametrized using ellipsoidal coordinates
x=asino cose, y=bsino sine, z=ccos, for 0≤0 ≤2л and 0 ≤ ≤л.
Show that the surface area S of the ellipsoid is
S =
2x
"²" sino √/a²b² cos² + c²(a² sin²0 + b² cos²0) sin² $ d& d$ .
(Note: The above double integral can not be evaluated by elementary means. For specific
values of a, b and c it can be evaluated using numerical methods. An alternative is to
express the surface area in terms of elliptic integrals.5)
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