Application of Integrals · Class 12 · CBSE · Science Mathematics

Find the area of the region bounded by the parabola y² = 4x and the line x = 1.

Practice question from Application of Integrals (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-D1728A

Find the area of the region bounded by the parabola y² = 4x and the line x = 1.

  1. A.2 square units
  2. B.8/3 square unitsCorrect answer
  3. C.4 square units
  4. D.16/3 square units

Solution

The parabola is x=y24x=\frac{y^2}{4} and meets x=1x=1 at y=±2y=\pm2. Hence, the area is ∫−22(1−y24)dy=83\int_{-2}^{2}\left(1-\frac{y^2}{4}\right)dy=\frac{8}{3} square units.

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