Question

evaluate triple integral of xyz dxdydz over the volume enclosed by the coordinate planes and the plane x/a+y/b+z/c=1​

Answer 1

Answer:

Using triple integrals and Cartesian coordinates, find the volume of the solid bounded by

xa+yb+zc=1

and the coordinate planes x=0,y=0,z=0

My take

I have set the parameters to

0≤x≤a

0≤y≤b(1−xa)

0≤z≤c(1−yb−xa)

and evaluated

∫a0∫b(1−xa)0∫c(1−yb−xa)01dzdydx

and gotten 0 as my final answer but the actal answer is abc/6

hope

it was helpful

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