Mathematics, 29.06.2019 16:30 darius7967
Use a parametrization to find the flux double integral from s ( f. n) dstd of f= 3zk across the portion of the sphere x^2+y^2+z^2=a^2 where y is positive in the direction away from the origin. * std = standard deviation symbol. the flux is
Answers: 1
:
![= 3a^3 \int^{\frac{\pi}{2}}_{\phi \to 0} \int^{2\pi}_{d \to 0} ( cos^2 \phi) \sin \phi d \theta d \phi \\\\= 3a^3 \int^{\frac{\pi}{2}}_{\phi \to 0} ([( - \frac{cos^3 \phi}{3})])^{2\pi}_{d \to 0} \ d \theta \\\\= 3a^3 \int^{\frac{\pi}{2}}_{\phi \to 0} ([( - \frac{cos^3 ({\frac{\pi}{2}}))} {3} + \frac{\cos^3 \ (0)}{3})]) \ d \theta \\\\= 3a^3 \int^{\frac{\pi}{2}}_{\phi \to 0} ([( - \frac{0}{3} + \frac{1}{3})]) \ d \theta \\\\= 3a^3 \int^{\frac{\pi}{2}}_{\phi \to 0} ([ \frac{1}{3}]) \ d \theta \\\\](/tpl/images/0031/6199/5ceb2.png)
, by
and 
. The domain of 
guarantees that we're dealing with only positive values of 
.
over 
pointing in the positive 
direction.
, 
, then
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Use a parametrization to find the flux double integral from s ( f. n) dstd of f= 3zk across the port...
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