The GATE Grind

GATE Calculus: Multiple Integrals – Previous Year Questions

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

  1. GATE 2021 MA Q48 (2 marks, Multiple choice) – V is bounded by y=x²+z² and y=4. Evaluate V15x2+z2\,dV.
  2. GATE 2023 MA Q30 (1 mark, Numerical answer) – If 14 -xx (x2+y2)-1dy\,dx= -/4/4 r-1dr\,d, find α.
  3. GATE 2025 MA Q30 (1 mark, Numerical answer) – Find the volume common to cylinders x²+y²≤4 and x²+z²≤4, to two decimals.
  4. GATE 2026 MA Q12 (1 mark, Multiple choice) – Reverse the integration order in I= 01 0 ydx\,dy+ 12 y-11dx\,dy.
  5. GATE 2026 MA Q64 (2 marks, Numerical answer) – On D=[0,2]×[0,2], let f(t)=⌈t⌉, the smallest integer at least t. Find D f(x+y)dx\,dy (integer).