A calculus problem by Hobart Pao

Calculus Level pending

Find the volume under the surface bounded by the planes z = x + 1 , z = x + 1 , z = y + 1 , z = y + 1 z=x+1, z=-x+1, z=y+1, z=-y+1 and above the x y xy plane. If the answer can be represented in the form a b \dfrac{a}{b} , where a , b a, b are coprime positive integers, find a + b a + b .


The answer is 5.

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