GATE 2014 EC (EC1) – Question 38
Find the volume under $z(x,y)=x+y$ above the triangle $0\le y\le x$, $0\le x\le12$.
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Correct answer: 862 to 866
Explanation
The triangle is0≤y≤x≤12. Integrate first over y:∫₀ˣ(x+y)dy=x²+x²/2=3x²/2. Then ∫₀¹²(3x²/2)dx=[x³/2]₀¹²=**864**. Treating the domain as a square would incorrectly include points above y=x.