GATE Engineering Mathematics: Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals – Previous Year Questions

7 GATE previous year questions on Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals (Engineering Mathematics, Civil Engineering) with answers and explanations, from every paper.

1. GATE 2023 CE (CE1) Q11 (1 mark, Multiple choice) – For the integral I = -111x2dx which of the following statements is TRUE?
2. GATE 2024 CE (CE2) Q44 (2 marks, Multiple select) – Three vectors p, q, and r are given as p = i + j + k, q = i + 2j + 3k, r = 2i + 3j + 4k Which of the following is/are CORRECT?
3. GATE 2024 CE (CE1) Q37 (2 marks, Multiple choice) – A vector field p and a scalar field r are given by p = (2x2 - 3xy + z2)i + (2y2 - 3yz + x2)j + (2z2 - 3xz + x2)k r = 6x2 + 4y2 - z2 - 9xyz - 2xy + 3xz…
4. GATE 2025 CE (CE2) Q12 (1 mark, Multiple choice) – Integration of (x) with x i.e., (x)\,dx = .
5. GATE 2025 CE (CE2) Q21 (1 mark, Multiple select) – Consider a velocity vector, V in (x, y, z) coordinates given below. Pick one or more CORRECT statements(s) from the choices given below. V = ux + vy
6. GATE 2026 CE (CE2) Q37 (2 marks, Multiple choice) – Vector field V is defined as V = 3x2yz\,i - 5xy\,j + 6yz2\,k The curl of V at point (2, -1, 1) is
7. GATE 2026 CE (CE1) Q36 (2 marks, Multiple choice) – Let f(x) be a continuous function defined in [0, 2] R and satisfying the equation 02 f(x)[x - f(x)]\,dx = 23. The value of f(1) is