GATE 2026 ES – Question 64
Find the first-quadrant area bounded by $y=8-x$ and the coordinate axes, in integer square units.
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Correct answer: 32 to 32
Explanation
The line meets the y-axis at $(0,8)$ and the x-axis at $(8,0)$. The bounded first-quadrant region is a right triangle with base and height both 8. Its area is $\frac12(8)(8)=\mathbf{32}$ square units. Equivalently,$\int_0^8(8-x)dx=32$.