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Friday, 9 October

JEE Main Maths · Class 12

Application of Integrals: JEE Main previous year questions

Application of Integrals had 39 questions in the 42 JEE Main shifts Lumi analysed, about 0.8 a shift, asked in 37 of 42 shifts. It ranks 17 of 22 Maths chapters by questions; 38% of its questions were hard.

Questions
39
in 37 of 42 shifts
A shift, on average
0.8
of 25 Maths questions
Since 2024
+0.0
0.8 a shift in 2017–23, 0.9 in 2024–26
Numerical answer
13
33% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
05101’174’203’213’225’238’246’259’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20204
  • 20213
  • 20223
  • 20235
  • 20248
  • 20256
  • 20269
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

1 topics and 12 distinct ideas; 4 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

1 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
4 repeat

Study it on Lumi

Application of Integrals: the interactive lesson

Every question

All 39 Application of Integrals questions

Newest first. Each opens with its options and the official answer.

2026 9 questions

  1. 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
  2. 4 Apr 2026, Shift 1 · Q18The area of the region {(x,y):y≤π−∣x∣, y≤∣xsin⁡x∣, y≥0}\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\} is:HardSingle correct
  3. 4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves x+3y2=0x+3y^2=0 and x+4y2=1x+4y^2=1 is equal to:EasySingle correct
  4. 5 Apr 2026, Shift 1 · Q16The area of the region R={(x,y):xy≤27, 1≤y≤x2}R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\} is equal to:MediumSingle correct
  5. 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
  6. 6 Apr 2026, Shift 1 · Q19The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\} is:MediumSingle correct
  7. 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
  8. 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
  9. 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

2025 6 questions

  1. 2 Apr 2025, Shift 1 · Q21If the area of the region {(x,y):∣4−x2∣≤y≤x2, y≤4, x≥0}\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\} is…HardNumerical value
  2. 3 Apr 2025, Shift 1 · Q25The area of the region bounded by the curve y=max⁡{∣x∣,x∣x−2∣}y = \max\{|x|, x|x-2|\}, the xx-axis and the lines x=−2x = -2 and x=4x = 4 is equal to ______MediumNumerical value
  3. 3 Apr 2025, Shift 2 · Q19The area of the region {(x,y):∣x−y∣≤y≤4x}\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\} isMediumSingle correct
  4. 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
  5. 7 Apr 2025, Shift 2 · Q20If the area of the region {(x,y):1+x2≤y≤min⁡{x+7, 11−3x}}\{(x,y): 1+x^2\le y\le \min\{x+7,\ 11-3x\}\} is AA, then 3A3A is equal toMediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q25Let the area of the bounded region {(x,y):0≤9x≤y2,y≥3x−6}\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\} be AA. Then 6A6A is equal to __________MediumNumerical value

2024 8 questions

  1. 6 Apr 2024, Shift 2 · Q11If the area of the region {(x,y):ax2≤y≤1x, 1≤x≤2, 0<a<1}\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\} is (log⁡e2)−17(\log_e 2)-\frac{1}{7} then…MediumSingle correct
  2. 8 Apr 2024, Shift 1 · Q27Let the area of the region enclosed by the curve y=min⁡{sin⁡x,cos⁡x}y=\min\{\sin x,\cos x\} and the xx-axis between x=−πx=-\pi to x=πx=\pi be AA. Then A2A^2…MediumNumerical value
  3. 9 Apr 2024, Shift 1 · Q9The parabola y2=4xy^2=4x divides the area of the circle x2+y2=5x^2+y^2=5 in two parts. The area of the smaller part is equal to :MediumSingle correct
  4. 9 Apr 2024, Shift 2 · Q10The area (in square units) of the region enclosed by the ellipse x2+3y2=18x^2+3y^2=18 in the first quadrant below the line y=xy=x isMediumSingle correct
  5. 29 Jan 2024, Shift 1 · Q25The area (in sq. units) of the part of the circle x2+y2=169x^2+y^2=169 which is below the line 5x−y=135x-y=13 is…HardNumerical value
  6. 30 Jan 2024, Shift 2 · Q26The area of the region enclosed by the parabola (y−2)2=x−1(y-2)^2 = x - 1, the line x−2y+4=0x - 2y + 4 = 0 and the positive coordinate axes is ________.MediumNumerical value
  7. 31 Jan 2024, Shift 1 · Q10The area of the region {(x,y):y2≤4x, x<4, xy(x−1)(x−2)(x−3)(x−4)>0, x≠3}\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\} isHardSingle correct
  8. 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

2023 5 questions

  1. 6 Apr 2023, Shift 1 · Q22Let the point (p,p+1)(p,p+1) lie inside the region E={(x,y):3−x≤y≤9−x2, 0≤x≤3}E=\left\{(x,y):3-x\le y\le\sqrt{9-x^2},\,0\le x\le3\right\}. If the set of all values of…MediumNumerical value
  2. 6 Apr 2023, Shift 1 · Q26If the area of the region S={(x,y):2y−y2≤x2≤2y, x≥y}S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\} is equal to n+2n+1−πn−1\frac{n+2}{n+1}-\frac{\pi}{n-1}, then the natural…HardNumerical value
  3. 8 Apr 2023, Shift 2 · Q27Let the area enclosed by the lines x+y=2x + y = 2, y=0y = 0, x=0x = 0 and the curve f(x)=min⁡{x2+34,1+[x]}f(x) = \min\left\{x^2 + \frac{3}{4}, 1 + [x]\right\}…HardNumerical value
  4. 11 Apr 2023, Shift 1 · Q9Area of the region {(x,y):x2+(y−2)2≤4, x2≥2y}\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\} isMediumSingle correct
  5. 13 Apr 2023, Shift 2 · Q11The area of the region {(x,y):x2≤y≤∣x2−4∣, y≥1}\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\} isHardSingle correct

2022 3 questions

  1. 25 Jul 2022, Shift 1 · Q8The area of the region given by A={(x,y):x2≤y≤min⁡{x+2, 4−3x}}A=\{(x,y):x^2\le y\le\min\{x+2,\,4-3x\}\} is :MediumSingle correct
  2. 24 Jun 2022, Shift 1 · Q29Let S be the region bounded by the curves y=x3y=x^3 and y2=xy^2=x. The curve y=2∣x∣y=2|x| divides S into two regions of areas R1R_1 and R2R_2. If…HardNumerical value
  3. 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

2021 3 questions

  1. 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
  2. 25 Jul 2021, Shift 1 · Q63The area (in sq. units) of the region, given by the set {(x,y)∈R×R∣x≥0, 2x2≤y≤4−2x}\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^2\le y\le4-2x\} is :EasySingle correct
  3. 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

2020 4 questions

  1. 8 Jan 2020, Shift 1 · Q61For a>0a>0, let the curves C1:y2=axC_1: y^2=ax and C2:x2=ayC_2: x^2=ay intersect at origin O and a point P. Let the line x=bx=b (0<b<a0<b<a) intersect the…HardSingle correct
  2. 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
  3. 2 Sep 2020, Shift 1 · Q62Area (in sq. units) of the region outside ∣x∣2+∣y∣3=1\frac{|x|}{2}+\frac{|y|}{3}=1 and inside the ellipse x24+y29=1\frac{x^{2}}{4}+\frac{y^{2}}{9}=1 is :MediumSingle correct
  4. 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

2017 1 questions

  1. 2 Apr 2017 (offline) · Q76The area (in sq. units) of the region {(x,y):x≥0, x+y≤3, x2≤4y and y≤1+x}\{(x,y):x\geq0,\ x+y\leq3,\ x^2\leq4y\ \text{and}\ y\leq1+\sqrt{x}\} is :HardSingle correct

Pattern: Asked most years.