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Saturday, 31 October

JEE Main · Maths · Application of Integrals

Area Between Curves

JEE Main asked Area Between Curves 22 times in 22 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Area Under Curves, in Application of Integrals (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
22
in 22 shifts
Years
7 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.30.60’170.17’200.10’210.14’220.14’230.23’240.13’250.56’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 2 in 12 shifts · 2024: 5 in 18 shifts · 2025: 1 in 8 shifts · 2026: 5 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20265 of 9
  • 20251 of 8
  • 20245 of 18
  • 20232 of 12
  • 20224 of 24
  • 20213 of 24
  • 20202 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Area enclosed between two curves
  • Area of region bounded by curves

Difficulty

Easy 3Medium 9Hard 10

6 of the 22 questions had a numerical answer.

Every question

All 22 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 8 Apr 2026, Shift 2 · Q18Let f:(1,∞)→Rf : (1, \infty) \to \mathbf{R} be a function defined as f(x)=x−1x+1f(x) = \frac{x-1}{x+1}. Let fi+1(x)=f(fi(x))f^{i+1}(x) = f\left(f^{i}(x)\right),…HardSingle correct
  2. 6 Apr 2026, Shift 2 · Q19The area of the region {(x,y):x2−8x≤y≤−x}\{(x,y): x^2-8x\le y\le -x\} is :EasySingle correct
  3. 6 Apr 2026, Shift 1 · Q20Let ee be the base of natural logarithm and let f:{1,2,3,4}→{1,e,e2,e3}f:\{1,2,3,4\}\to\{1,e,e^2,e^3\} and…HardSingle correct
  4. 5 Apr 2026, Shift 2 · Q24Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function such that f(x)+3f(π2−x)=sin⁡xf(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x, x∈Rx \in \mathbf{R}. Let the maximum…HardNumerical value
  5. 2 Apr 2026, Shift 2 · Q24If the area of the region bounded by 16x2−9y2=14416x^2 - 9y^2 = 144 and 8x−3y=248x - 3y = 24 is AA, then 3(A+6log⁡e(3))3(A + 6\log_e(3)) is equal toHardNumerical value
  6. 7 Apr 2025, Shift 1 · Q19If the area of the region bounded by the curves y=4−x24y = 4 - \frac{x^2}{4} and y=x−42y = \frac{x-4}{2} is equal to α\alpha, then 6α6\alpha equalsEasySingle correct
  7. 31 Jan 2024, Shift 2 · Q11The area of the region enclosed by the parabolas y=4x−x2y=4x-x^2 and 3y=(x−4)23y=(x-4)^2 is equal toMediumSingle correct
  8. 1 Feb 2024, Shift 1 · Q9The area enclosed by the curves xy+4y=16xy+4y=16 and x+y=6x+y=6 is equal to :MediumSingle correct
  9. 8 Apr 2024, Shift 2 · Q12The area of the region in the first quadrant inside the circle x2+y2=8x^2 + y^2 = 8 and outside the parabola y2=2xy^2 = 2x is equal to :MediumSingle correct
  10. 6 Apr 2024, Shift 1 · Q12Let the area of the region enclosed by the curves y=3xy=3x, 2y=27−3x2y=27-3x and y=3x−xxy=3x-x\sqrt{x} be AA. Then 10A10A is equal toMediumSingle correct
  11. 4 Apr 2024, Shift 1 · Q13One of the points of intersection of the curves y=1+3x−2x2y=1+3x-2x^2 and y=1xy=\frac{1}{x} is (12,2)\left(\frac{1}{2}, 2\right). Let the area of the…HardSingle correct
  12. 15 Apr 2023, Shift 1 · Q27If the area bounded by the curve 2y2=3x2y^2=3x, lines x+y=3x+y=3, y=0y=0 and outside the circle (x−3)2+y2=2(x-3)^2+y^2=2 is A, then 4(π+4A)4(\pi+4A) is equal to…HardNumerical value
  13. 10 Apr 2023, Shift 1 · Q28Let y=p(x)y=p(x) be the parabola passing through the points (−1,0)(-1,0), (0,1)(0,1) and (1,0)(1,0). If the area of the region…HardNumerical value
  14. 29 Jun 2022, Shift 1 · Q6The area enclosed by y2=8xy^2 = 8x and y=2 xy = \sqrt{2}\,x that lies outside the triangle formed by y=2 xy = \sqrt{2}\,x, x=1x = 1,…MediumSingle correct
  15. 30 Jul 2022, Shift 2 · Q85If the area enclosed by the curves y=x2y = x^2, y3=xy^3 = x, x=−1x = -1 and y=x2y = x^2, y3=xy^3 = x, x=1x = 1, above the line x=2yx = 2y is…HardNumerical value
  16. 27 Jul 2022, Shift 2 · Q8The area of the region enclosed by y≤4x2y \leq 4x^2, x2≤9yx^2 \leq 9y and y≤4y \leq 4, is equal to :MediumSingle correct
  17. 27 Jul 2022, Shift 1 · Q9The area of the smaller region enclosed by the curves y2=8x+4y^2 = 8x + 4 and x2+y2+43x−4=0x^2 + y^2 + 4\sqrt{3}x - 4 = 0 is equal toHardSingle correct
  18. 16 Mar 2021, Shift 2 · Q80Let C1C_1 be the curve obtained by the solution of differential equation 2xydydx=y2−x22xy\frac{dy}{dx}=y^2-x^2, x>0x>0. Let the curve C2C_2 be the…HardSingle correct
  19. 24 Feb 2021, Shift 1 · Q71The area (in sq. units) of the part of the circle x2+y2=36x^2 + y^2 = 36, which is outside the parabola y2=9xy^2 = 9x, is :MediumSingle correct
  20. 3 Aug 2021, Shift 2 · Q85If the area (in sq. units) bounded by the parabolas 5x2−y=05x^2 - y = 0 and 2x2−y+b=02x^2 - y + b = 0 (b>0)(b > 0) is 12312\sqrt{3}, then 'bb' is equal…MediumNumerical value
  21. 6 Sep 2020, Shift 2 · Q62The area (in sq. units) of the region enclosed by the curves y=x2−1y=x^2-1 and y=1−x2y=1-x^2 is equal to :EasySingle correct
  22. 9 Jan 2020, Shift 2 · Q63Given : f(x)={x,0≤x<1212,x=121−x,12<x≤1f(x)=\begin{cases}x, & 0\le x<\frac{1}{2}\\ \frac{1}{2}, & x=\frac{1}{2}\\ 1-x, & \frac{1}{2}<x\le1\end{cases} and…MediumSingle correct

Shifts: 9 Jan 2020, Shift 2, 6 Sep 2020, Shift 2, 24 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 3 Aug 2021, Shift 2, 29 Jun 2022, Shift 1, 27 Jul 2022, Shift 2, 27 Jul 2022, Shift 1, 30 Jul 2022, Shift 2, 10 Apr 2023, Shift 1, 15 Apr 2023, Shift 1, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 1, 4 Apr 2024, Shift 1, 6 Apr 2024, Shift 1, 8 Apr 2024, Shift 2, 7 Apr 2025, Shift 1, 2 Apr 2026, Shift 2, 5 Apr 2026, Shift 2, 6 Apr 2026, Shift 2, 6 Apr 2026, Shift 1, 8 Apr 2026, Shift 2.

Same topic

Other ideas in Area Under Curves

Area Under Curves has 24 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas