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GATE 2016 CE (CE2) – Question 39

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 2 marks · Numerical answer

The area between $x^2=8y$ and the line $y=8$ is ______.

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Correct answer: 85.0 to 85.5

Explanation

The line meets the parabola at x=±8. Integrate upper minus lower ordinate: area=∫−8⁸(8−x²/8)dx. Evaluation gives128−128/3=256/3=**85.333square units**. Symmetry also permits twice the integral from0 to8.