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.

Following are the solution to the given expression:

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I gather you're supposed to compute the integral of over a surface that is the part of the parabolic cylinder with and .

We can parameterize by

with the given constraints on and . Take the normal vector to to be

so that the surface element is

Then in the integral, we have

c. side angle side. u shares the same sides

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.