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NDA 2021 Maths · Mathematics · Application of Integrals · hard

The area of the region enclosed by the parabola y=x^2 and the line y=2-x is

Single correct option

The area of the region enclosed by the parabola y=x2y=x^2 and the line y=2−xy=2-x is
  1. A. 92\dfrac92 square units
  2. B. 94\dfrac{9}{4} square units
  3. C. 72\dfrac{7}{2} square units
  4. D. 32\dfrac{3}{2} square units
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Answer: (A) 92\dfrac92 square units

Solve x2=2−xx^2=2-x: x=−2x=-2 or x=1x=1. The line lies above the parabola between them, so area =∫−21(2−x−x2) dx=[2x−x22−x33]−21=76+103=92=\int_{-2}^{1}(2-x-x^2)\,dx=\left[2x-\dfrac{x^2}{2}-\dfrac{x^3}{3}\right]_{-2}^{1}=\dfrac76+\dfrac{10}{3}=\dfrac92.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake