Mathematics, 12.12.2019 20:31 TURBONTRO1047
Integrate g(x, y,z)equalsz over the parabolic cylinder yequalszsquared, 0less than or equalsxless than or equals2, 0less than or equalszless than or equalsstartfraction startroot 15 endroot over 2 endfraction . write the integral modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper s upper g (x comma y comma z )d sigma as a double integral. modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper s upper g (x comma y comma z )d sigmaequalsintegral from nothing to nothing integral from nothing to nothing nothing dz dx.
Answers: 1
![= \int^{4}_{0} [\frac{1}{12}(1+4z^2)^{\frac{3}{2}}]^{\frac{\sqrt{15}}{2}}_{0} \ dx\\\\= \int^{4}_{0} [\frac{1}{12}(4(\frac{\sqrt{15}}{2})^2 +1)^{\frac{3}{2}} - \frac{1}{12}(4(0)^2 +1)^{\frac{3}{2}}]\ dx\\\\= \int^{4}_{0} [\frac{21}{4}]\ dx\\\\= [\frac{21}{4}] \ \int^{4}_{0} \ dx\\\\= [\frac{21}{4}] \ [x]^{4}_{0} \\\\= [\frac{21}{4}] \ [4-0] \\\\= \frac{21}{4} \times 4 \\\\= 21\\\\](/tpl/images/0415/6905/b1d25.png)
over a surface 
that is the part of the parabolic cylinder 
with 
and 
.
and 
. Take the normal vector to 
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Integrate g(x, y,z)equalsz over the parabolic cylinder yequalszsquared, 0less than or equalsxless th...
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