The GATE Grind

GATE 2022 ST – Question 40

Calculus · Multiple Integrals · 2 marks · Multiple choice

The line y=αx,α≥√2,divides R={(x,y):0≤x≤√y,0≤y≤2} into equal areas. Find α.

  1. 3/√2
  2. 2√2
  3. √2
  4. 5/(2√2)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 3/√2

Explanation

The total area is ∫₀²√y dy=4√2/3. Since α≥√2,the line x=y/α lies inside each horizontal slice. The area on its left is ∫₀²y/α dy=2/α. Equal division requires 2/α=2√2/3,so **α=3/√2, A**.

More Multiple Integrals questions

All Multiple Integrals questions →