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GATE 2016 CE (CE1) – Question 38

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

The area enclosed by $y=x^2+1$ and $x+y=3$ is ______.

  1. 59/6
  2. 9/2
  3. 10/3
  4. 7/6

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Correct answer: (B) 9/2

Explanation

Intersections satisfy3−x=x²+1, or(x+2)(x−1)=0, so bounds are−2 and1. The line lies above the parabola on this interval. Area is the integral of2−x−x², giving[2x−x²/2−x³/3]−2 to1=9/2. Thus **9/2 square units, B**.