GATE 2020 ST – Question 61

Calculus · Multiple Integrals · 2 marks · Numerical answer

On $D=\{(x,y,z):0\le x,y,z\le1,\ x+y+z\le1\}$ let $I=\iiint_D(x+y)\,dx\,dy\,dz$. Find84I.

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Correct answer: 7 to 7

Explanation

The unit tetrahedron has volume1/6 and centroid(1/4,1/4,1/4). Integrating its linear coordinate function gives I=(1/6)(1/4+1/4)=1/12. Equivalently, direct iterated integration gives the same value. Thus84I=7.

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