GATE Engineering Mathematics: Calculus: Definite and improper integrals, partial and total derivatives, maxima and minima – Previous Year Questions

4 GATE previous year questions on Calculus: Definite and improper integrals, partial and total derivatives, maxima and minima (Engineering Mathematics, Chemical Engineering) with answers and explanations, from every paper.

1. GATE 2022 CH Q14 (1 mark, Multiple choice) – The value of the real variable x 0, which maximizes the function f(x) = xe e-x is
2. GATE 2023 CH Q48 (2 marks, Numerical answer) – The first derivative of the function U(r) = 4[(1r)12 - (1r)6] evaluated at r = 1 is (in integer).
3. GATE 2024 CH Q47 (2 marks, Multiple choice) – Let r and be the polar coordinates defined by x = r and y = r. The area of the cardioid r = a(1 - ), 0 2, is
4. GATE 2026 CH Q41 (2 marks, Multiple choice) – Consider the following curve in polar coordinates. r = 2 - 2 Which one of the following is the area enclosed by the curve for 0 2 ?