GATE 2025 MN – Question 58
Find the area enclosed by $y=\sqrt x$ and $y=8x^2$,to three decimals.
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Correct answer: 0.030 to 0.050
Explanation
The intersections satisfy√x=8x²,giving x=0 and1/4. On that interval√x is above8x². Integrate:[(2/3)x^(3/2)−(8/3)x³] from0 to1/4=1/12−1/24=1/24≈0.041667. Rounded area is0.042.