example of integration over sphere with respect to surface area
As an example of how to use the formula derived in http://planetmath.org/node/6664example 1, let us consider the following example:
∫S(sinucosv-sinv)2d2A=∫2π0∫π0(sinucosv-sinv)2sinududv= |
∫2π0∫π0(sin3ucos2v-2sin2usinvcosv+sinusin2v)𝑑u𝑑v= |
∫2π0(2cos2v-23cos2v-πsinvcosv+2sin2v)𝑑v= |
2π-2π3-0+2π=10π3 |
To return to the main entry http://planetmath.org/node/6660click here.
Title | example of integration over sphere with respect to surface area |
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Canonical name | ExampleOfIntegrationOverSphereWithRespectToSurfaceArea |
Date of creation | 2013-03-22 14:57:58 |
Last modified on | 2013-03-22 14:57:58 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 5 |
Author | rspuzio (6075) |
Entry type | Example |
Classification | msc 28A75 |