Evaluate the integralover the volume enclosed by three coordinate planes and the plane x + y + z = 1.Correct answer is '0.0013'. Can you explain this answer?

Question

Answer

The given plane x + y + z = 1 meets the co ordinate axes a tA (1 , 0, 0) B ( 0 , 1, 0) and C(0, 0, 1).
Here a column parallel to z-axis is bounded by the plane z = 0 and z = 1 - x - y. Also the region S above which the volume V stands is the triangle OAB bounded by the lines y = 0, x = 0 and x + y = 1 (on xy plane )

Hence the given integral

on simplifying

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