Applications of Integrals: Class 12 Previous Year Questions

Applications of Integrals questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Find the area of the region bounded by the curve 2 4 y x  , y -axis and line 3 y  .
   CBSE practice 2023-242 marksshort answerRepeated: 2023,2026
2. The area bounded by the curve y = x| x |, x-axis and the ordinates x = –1 and x = 1 is given by 1 (A) 0 (B) 3 1 (C) 3 2 (D) 3 4 dx
   Board 20261 markMCQ
3. Sketch the graph of y = I x + 3 I and find the area of the region enclosed by the curve, x-axis, between x = -6 and x = O, using integration.
   Board 20253 marksshort answer
4. The area of the shaded region bounded by the curves y2 = x, x = 4 and the x-axis is given by 1 =4 -1 (A) xp x (B) dy Vx dx (D) (C) Vx dx Page 9 of 24 (A) (B) ·/2 ·/2 ··/2 ·/2 (C) (D) ·/2 -1 10 19 20·1 (A),(B),(C) (D)1 (A) (A) (R) (R), (A) (B), (A) (R) (R), (A)…
   Board 20251 markMCQ
5. Using integration, find the area of region bounded by line y = V3x, the curve y = 4 - x2 and y-axis in first quadrant.
   Board 20235 markslong answer
6. (A). Using Integration, find the area of the region {(𝑥, 𝑦): 0 ≤𝑦≤√4 −𝑥2 , 𝑥≥2 −𝑦}. 5 OR Q34 (B). Using Integration, find the area of the region bounded by the curve 𝑦2 = 2𝑥 and the line 𝑥−2𝑦= 0. *There is no change in the Question Paper Design and Assessment …
   Sample paper 2026-275 markslong answer
7. Shown below is the curve defined by the equation y = log (x + 1) for x ≥ 0. Which of these is the area of the shaded region? (a) 6log(2) - 2 (b) 6log(2) - 6 (c) 6log(2) (d) 5log(2)
   CBSE practice 2023-241 markMCQ
8. Shown below is an ellipse whose equation is 𝑥2 81 + 𝑦2 36 = 1. Find the area of the shaded region in terms of π. Show your steps.
   CBSE practice 2022-235 markslong answer
9. The points D, E and F are the mid-points of AB, BC and CA respectively. (Note: The figure is not to scale.) What is the area of the shaded region? (a) 2 sq units (b) 3 2 sq units (c) 1 2 sq units (d) (2√26 - 1) sq units
   CBSE practice 2023-241 markMCQ
10. Shown below is a parabola. Find the area of the shaded region. Show your steps. (Note: Take √2 as 1.4 and √3 as 1.7.) OR Shown below is the graph of f(x) = 2x2 in the first quadrant. Find the area of the shaded region. Show your steps. (Note: You need not eval…
    CBSE practice 2021-224 marksshort answer

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