GATE Calculus: Multiple Integrals – Previous Year Questions

6 GATE previous year questions on Multiple Integrals (Calculus, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q21 (1 mark, Numerical answer) – Let I=4 1/21 1-x2x1x2+y2\,dy\,dx. Find eI+,to two decimals.
2. GATE 2022 ST Q40 (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.
3. GATE 2023 ST Q11 (1 mark, Multiple choice) – Find the area bounded by x=−y² and y=x+2.
4. GATE 2024 ST Q11 (1 mark, Multiple choice) – D is bounded by y=x and y=4x−x². Find ∬ D x dxdy.
5. GATE 2025 ST Q25 (1 mark, Numerical answer) – Evaluate I=2 01 01 y2[(1+xy)]dx\,dy (integer).
6. GATE 2026 ST Q61 (2 marks, Numerical answer) – On D=(x,y):0<x²+y²≤1, let I α=∬ D(x²+y²)(−α)dxdy,α≥0. Find N₀=supα≥0:I α<∞ (integer).