JEE Main · Maths · Application of Integrals
Area Under Curves: JEE Main previous year questions
94 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 36 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 94
- in 87 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.9
- model; history: 0.8 a shift on average, typically 0.6–0.9
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 87 of 108 shifts: 94 questions, #8 of 196 topics. It came in every year with analysed shifts.
- 02
31% of its questions since 2020 tested an idea no earlier year had asked; 52 repeated an idea from the year before.
- 03
The most repeated idea is Area Between Curves, asked 22 times in 22 shifts (2020, 2021, 2022, 2023, 2024, 2025, 2026), most often as “area enclosed between two curves”.
- 04
JEE Main has asked 24 of the 65 ideas in this topic; 32 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (63%); 36% need a numerical answer, 12% are easy and 33% hard. It went up from 0.7 to 0.9 questions a shift since 2024.
- 06
The skill tested most is multi-step (51%), then calculation (45%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 1 in 1 shift · 2020: 7 in 12 shifts · 2021: 15 in 24 shifts · 2022: 23 in 24 shifts · 2023: 12 in 12 shifts · 2024: 20 in 18 shifts · 2025: 7 in 8 shifts · 2026: 9 in 9 shifts.
- Up to 2023
- 0.7
- a shift, of 25
- Since 2024
- 0.9
- 0.2
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 87/108
- 81% of analysed shifts
Recent framings
- area bounded by curve, line and axis
- area of region from system of inequalities
- numerical: area between curves from defined function
Revise first
- Area Between Curves · asked 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Area of Inequalities · asked 2017, 2020, 2021, 2022, 2023, 2024, 2025, 2026
- Area Involving Max/Min Functions · asked 2021, 2022, 2023, 2024, 2025, 2026
How it is asked
Difficulty, format and skill
Across all 94 questions on Area Under Curves since 2017.
Difficulty
QUESTIONS- Easy11 · 12%
- Medium52 · 55%
- Hard31 · 33%
Format
SHARE- Single correct · 59 Q63%
- Numerical value · 34 Q36%
- Diagram based · 1 Q1%
Skill tested
SHARE- Multi-step · 48 Q51%
- Calculation · 42 Q45%
- Application · 4 Q4%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 24 of the 65 ideas in this topic. 32 have never been asked yet.
- Asked directly24 · 37%
- Touched inside another question9 · 14%
- Never asked32 · 49%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
22 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
24 different ideas were tested; 14 came more than once.
area enclosed between two curves
Single correct · 22 shifts · 6 numericalarea of region defined by inequalities
Single correct · 15 shifts · 5 numericalarea bounded by parabola and min of lines
Numerical value · 8 shifts · 4 numericalarea bounded by modulus curve and line
Single correct · 7 shifts · 2 numericalarea enclosed between two curves
Single correct · 6 shifts · 2 numericalarea between curves
Numerical value · 6 shifts · 3 numericalarea bounded by tangent, parabola and axis
Single correct · 3 shifts · 1 numericalidentify differential equation from family of curves
Diagram based · 3 shifts · 1 numericalarea bounded by parabola, line and axes
Numerical value · 3 shifts · 2 numericalarea bisected by line between parabolas
Single correct · 3 shifts · 1 numericalarea of region with unknown parameter
Numerical value · 2 shifts · 1 numericalarea of smaller part cut from circle
Numerical value · 2 shifts · 1 numericalarea of region defined by inequalities
Numerical value · 2 shifts · 1 numericalarea between trigonometric curves and axes
Numerical value · 2 shifts · 1 numericalarea of circle segment cut by line
Numerical value · 1 shift · 1 numericalminimum ratio of areas on parabola
Numerical value · 1 shift · 1 numericalarea of region bounded by ellipse and line
Single correct · 1 shiftarea enclosed by curve and its tangent
Single correct · 1 shiftarea enclosed by a locus and a line
Single correct · 1 shiftarea of region bounded by curves and axes
Single correct · 1 shiftarea between logarithmic curves
Single correct · 1 shiftarea integral rewritten with horizontal strips
Single correct · 1 shiftarea of closed loop of algebraic curve
Single correct · 1 shiftarea bounded by cubic between its extrema
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Area Between Curvesarea enclosed between two curves | 22 | 22 | Single correctMulti-step | 6 | |
| Area of Inequalitiesarea of region defined by inequalities | 15 | 15 | Single correctMulti-step | 5 | |
| Area Involving Max/Min Functionsarea bounded by parabola and min of lines | 8 | 8 | Numerical valueCalculation | 4 | |
| Area with Modulusarea bounded by modulus curve and line | 7 | 7 | Single correctCalculation | 2 | |
| Area Between Two Standard Parabolasarea enclosed between two curves | 6 | 6 | Single correctCalculation | 2 | |
| Area Between Parabola and Linearea between curves | 6 | 6 | Numerical valueCalculation | 3 | |
| Area Involving Tangents and Normalsarea bounded by tangent, parabola and axis | 3 | 3 | Single correctMulti-step | 1 | |
| Curves from Area Propertiesidentify differential equation from family of curves | 3 | 3 | Diagram basedMulti-step | 1 | |
| Regions with Multiple Bounding Curvesarea bounded by parabola, line and axes | 3 | 3 | Numerical valueCalculation | 2 | |
| Bisection of Bounded Areasarea bisected by line between parabolas | 3 | 3 | Single correctMulti-step | 1 | |
| Finding Unknown Parameters from Areaarea of region with unknown parameter | 2 | 2 | Numerical valueCalculation | 1 | |
| Ratio of Divided Areasarea of smaller part cut from circle | 2 | 2 | Numerical valueMulti-step | 1 | |
| Area of Ellipse and Sectorsarea of region defined by inequalities | 2 | 2 | Numerical valueMulti-step | 1 | |
| Area Between Trigonometric Curvesarea between trigonometric curves and axes | 2 | 2 | Numerical valueCalculation | 1 | |
| Area of Ellipse and its Segmentsarea of circle segment cut by line | 1 | 1 | Numerical valueCalculation | 1 | |
| Area of Parabolic Segmentminimum ratio of areas on parabola | 1 | 1 | Numerical valueMulti-step | 1 | |
| Ellipse Segment Area via Eccentric Anglearea of region bounded by ellipse and line | 1 | 1 | Single correctApplication | – | |
| Area Between Cubic Curve and Tangentarea enclosed by curve and its tangent | 1 | 1 | Single correctMulti-step | – | |
| Area of Locus-Defined Regionsarea enclosed by a locus and a line | 1 | 1 | Single correctMulti-step | – | |
| Area with Y-Axisarea of region bounded by curves and axes | 1 | 1 | Single correctCalculation | – | |
| Exponential and Logarithmic Bounded Regionsarea between logarithmic curves | 1 | 1 | Single correctCalculation | – | |
| Optimal Strip Selection (dx vs dy)area integral rewritten with horizontal strips | 1 | 1 | Single correctApplication | – | |
| Area of Algebraic Curve Loopsarea of closed loop of algebraic curve | 1 | 1 | Single correctMulti-step | – | |
| Area with X-Axisarea bounded by cubic between its extrema | 1 | 1 | Numerical valueMulti-step | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Area Under Curves questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20269 questions in 8 shifts
- 2 Apr, Shift 2Q24If the area of the region bounded by and is , then is equal to
Idea: Area Between Curves
Asked the year beforeHardNumerical value - 4 Apr, Shift 1Q18The area of the region is:
Idea: Area Involving Max/Min Functions
Asked the year beforeHardSingle correct - 4 Apr, Shift 2Q18The area of the region bounded by the curves and is equal to:
Idea: Area Between Two Standard Parabolas
EasySingle correct - 5 Apr, Shift 1Q16The area of the region is equal to:
Idea: Area of Inequalities
Asked the year beforeMediumSingle correct - 5 Apr, Shift 2Q24Let be a function such that , . Let the maximum…
Idea: Area Between Curves
Asked the year beforeHardNumerical value - 6 Apr, Shift 1Q19The area of the region is:
Idea: Area of Inequalities
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q20Let be the base of natural logarithm and let and…
Idea: Area Between Curves
Asked the year beforeHardSingle correct - 6 Apr, Shift 2Q19The area of the region is :
Idea: Area Between Curves
Asked the year beforeEasySingle correct - 8 Apr, Shift 2Q18Let be a function defined as . Let ,…
Idea: Area Between Curves
Asked the year beforeHardSingle correct
JEE Main 20257 questions in 7 shifts
- 2 Apr, Shift 1Q21If the area of the region is…
Idea: Area with Modulus
Asked the year beforeHardNumerical value - 3 Apr, Shift 1Q25The area of the region bounded by the curve , the -axis and the lines and is equal to ______
Idea: Area Involving Max/Min Functions
Asked the year beforeMediumNumerical value - 3 Apr, Shift 2Q19The area of the region is
Idea: Area of Inequalities
Asked the year beforeMediumSingle correct - 4 Apr, Shift 2Q19A line passing through the point , touches the parabola at the point B in the first quadrant. The area, of the region…
Idea: Area Involving Tangents and Normals
MediumSingle correct - 7 Apr, Shift 1Q19If the area of the region bounded by the curves and is equal to , then equals
Idea: Area Between Curves
Asked the year beforeEasySingle correct - 7 Apr, Shift 2Q20If the area of the region is , then is equal to
Idea: Area Involving Max/Min Functions
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q25Let the area of the bounded region be . Then is equal to __________
Idea: Area of Inequalities
Asked the year beforeMediumNumerical value
JEE Main 202420 questions in 18 shifts
- 4 Apr, Shift 1Q13One of the points of intersection of the curves and is . Let the area of the…
Idea: Area Between Curves
Asked the year beforeHardSingle correct - 4 Apr, Shift 2Q11The area (in sq. units) of the region described by is
Idea: Area Between Parabola and Line
MediumSingle correct - 5 Apr, Shift 1Q27The area of the region enclosed by the parabolas and is ________.
Idea: Area Between Two Standard Parabolas
EasyNumerical value - 5 Apr, Shift 2Q12The area enclosed between the curves and is :
Idea: Area with Modulus
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q12Let the area of the region enclosed by the curves , and be . Then is equal to
Idea: Area Between Curves
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q11If the area of the region is then…
Idea: Finding Unknown Parameters from Area
MediumSingle correct - 8 Apr, Shift 1Q12Let be a positive function such that the area bounded by , from to is . Then the…
Idea: Curves from Area Properties
HardSingle correct - 8 Apr, Shift 1Q27Let the area of the region enclosed by the curve and the -axis between to be . Then …
Idea: Area Involving Max/Min Functions
Asked the year beforeMediumNumerical value - 8 Apr, Shift 2Q12The area of the region in the first quadrant inside the circle and outside the parabola is equal to :
Idea: Area Between Curves
Asked the year beforeMediumSingle correct - 9 Apr, Shift 1Q9The parabola divides the area of the circle in two parts. The area of the smaller part is equal to :
Idea: Ratio of Divided Areas
MediumSingle correct - 9 Apr, Shift 2Q10The area (in square units) of the region enclosed by the ellipse in the first quadrant below the line is
Idea: Ellipse Segment Area via Eccentric Angle
New ideaMediumSingle correct - 1 Feb, Shift 1Q9The area enclosed by the curves and is equal to :
Idea: Area Between Curves
Asked the year beforeMediumSingle correct - 1 Feb, Shift 2Q26The sum of squares of all possible values of , for which area of the region bounded by the parabolas and is…
Idea: Area Between Two Standard Parabolas
HardNumerical value - 1 Feb, Shift 2Q28Three points , , , , , are on the parabola . Let be the area of the region bounded by…
Idea: Area of Parabolic Segment
New ideaHardNumerical value - 27 Jan, Shift 1Q26Let the area of the region be , where m and n are coprime…
Idea: Area of Inequalities
Asked the year beforeMediumNumerical value - 29 Jan, Shift 1Q25The area (in sq. units) of the part of the circle which is below the line is…
Idea: Area of Ellipse and its Segments
New ideaHardNumerical value - 30 Jan, Shift 1Q11The area (in square units) of the region bounded by the parabola and the line , is :
Idea: Area Between Parabola and Line
MediumSingle correct - 30 Jan, Shift 2Q26The area of the region enclosed by the parabola , the line and the positive coordinate axes is ________.
Idea: Regions with Multiple Bounding Curves
Asked the year beforeMediumNumerical value - 31 Jan, Shift 1Q10The area of the region is
Idea: Area of Inequalities
Asked the year beforeHardSingle correct - 31 Jan, Shift 2Q11The area of the region enclosed by the parabolas and is equal to
Idea: Area Between Curves
Asked the year beforeMediumSingle correct
JEE Main 202312 questions in 12 shifts
- 6 Apr, Shift 1Q26If the area of the region is equal to , then the natural…
Idea: Area of Inequalities
Asked the year beforeHardNumerical value - 6 Apr, Shift 2Q14The area bounded by the curves and is equal to
Idea: Area with Modulus
Asked the year beforeEasySingle correct - 8 Apr, Shift 1Q12The area of the region is
Idea: Regions with Multiple Bounding Curves
MediumSingle correct - 8 Apr, Shift 2Q27Let the area enclosed by the lines , , and the curve …
Idea: Area Involving Max/Min Functions
Asked the year beforeHardNumerical value - 10 Apr, Shift 1 · Q28Area Between CurvesAsked the year beforeHard
- 10 Apr, Shift 2 · Q26Area with ModulusAsked the year beforeMedium
- 11 Apr, Shift 1 · Q9Area of InequalitiesAsked the year beforeMedium
- 11 Apr, Shift 2 · Q25Area Involving Tangents and NormalsMedium
- 12 Apr, Shift 1 · Q10Area Between Cubic Curve and TangentNew ideaMedium
- 13 Apr, Shift 1 · Q12Area Involving Max/Min FunctionsAsked the year beforeMedium
- 13 Apr, Shift 2 · Q11Area of InequalitiesAsked the year beforeHard
- 15 Apr, Shift 1 · Q27Area Between CurvesAsked the year beforeHard
JEE Main 202223 questions in 19 shifts
- 25 Jul, Shift 1 · Q8Area Involving Max/Min FunctionsAsked the year beforeMedium
- 25 Jul, Shift 1 · Q13Area of Locus-Defined RegionsNew ideaMedium
- 26 Jul, Shift 1 · Q5Area with Y-AxisNew ideaMedium
- 26 Jul, Shift 1 · Q27Curves from Area PropertiesNew ideaHard
- 26 Jul, Shift 2 · Q20Area with ModulusNew ideaMedium
- 27 Jul, Shift 1 · Q9Area Between CurvesAsked the year beforeHard
- 27 Jul, Shift 2 · Q8Area Between CurvesAsked the year beforeMedium
- 27 Jul, Shift 2 · Q10Curves from Area PropertiesNew ideaHard
- 28 Jul, Shift 2 · Q70Exponential and Logarithmic Bounded RegionsNew ideaHard
- 29 Jul, Shift 1 · Q16Area with ModulusNew ideaMedium
- 30 Jul, Shift 2 · Q85Area Between CurvesAsked the year beforeHard
- 24 Jun, Shift 1 · Q29Ratio of Divided AreasNew ideaHard
- 24 Jun, Shift 2 · Q26Area Between Parabola and LineAsked the year beforeEasy
- 25 Jun, Shift 2 · Q6Area Between Two Standard ParabolasAsked the year beforeMedium
- 26 Jun, Shift 2 · Q7Area Between Two Standard ParabolasAsked the year beforeMedium
- 27 Jun, Shift 1 · Q26Area of InequalitiesAsked the year beforeHard
- 27 Jun, Shift 2 · Q27Area of InequalitiesAsked the year beforeHard
- 28 Jun, Shift 1 · Q9Area of InequalitiesAsked the year beforeMedium
- 28 Jun, Shift 2 · Q9Area with ModulusNew ideaMedium
- 29 Jun, Shift 1 · Q6Area Between CurvesAsked the year beforeMedium
- 29 Jun, Shift 2 · Q8Optimal Strip Selection (dx vs dy)New ideaMedium
- 29 Jun, Shift 2 · Q25Area of Ellipse and SectorsMedium
- 30 Jun, Shift 1 · Q24Finding Unknown Parameters from AreaNew ideaHard
JEE Main 202115 questions in 15 shifts
- 3 Aug, Shift 1 · Q87Area Between Parabola and LineAsked the year beforeEasy
- 3 Aug, Shift 2 · Q85Area Between CurvesAsked the year beforeMedium
- 26 Aug, Shift 1 · Q85Area Between Parabola and LineAsked the year beforeMedium
- 26 Aug, Shift 2 · Q85Area with X-AxisNew ideaMedium
- 27 Aug, Shift 2 · Q71Area Involving Tangents and NormalsNew ideaMedium
- 31 Aug, Shift 2 · Q87Bisection of Bounded AreasAsked the year beforeMedium
- 24 Feb, Shift 1 · Q71Area Between CurvesAsked the year beforeMedium
- 24 Feb, Shift 2 · Q80Area Between Two Standard ParabolasNew ideaEasy
- 25 Feb, Shift 1 · Q88Area Between Trigonometric CurvesNew ideaMedium
- 26 Feb, Shift 2 · Q63Area Between Trigonometric CurvesNew ideaMedium
- 22 Jul, Shift 2 · Q83Regions with Multiple Bounding CurvesNew ideaHard
- 25 Jul, Shift 1 · Q63Area of InequalitiesAsked the year beforeEasy
- 16 Mar, Shift 2 · Q80Area Between CurvesAsked the year beforeHard
- 17 Mar, Shift 2 · Q87Area Involving Max/Min FunctionsNew ideaMedium
- 18 Mar, Shift 2 · Q70Area of Algebraic Curve LoopsNew ideaHard
JEE Main 20207 questions in 7 shifts
- 8 Jan, Shift 1 · Q61Bisection of Bounded AreasNew ideaHard
- 8 Jan, Shift 2 · Q62Area Between Parabola and LineNew ideaEasy
- 9 Jan, Shift 2 · Q63Area Between CurvesNew ideaMedium
- 2 Sep, Shift 1 · Q62Area of Ellipse and SectorsNew ideaMedium
- 2 Sep, Shift 2 · Q62Bisection of Bounded AreasNew ideaMedium
- 3 Sep, Shift 1 · Q61Area of InequalitiesAsked the year beforeMedium
- 6 Sep, Shift 2 · Q62Area Between CurvesNew ideaEasy
JEE Main 20171 question in 1 shift
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.
More topics in Application of Integrals
This is the only topic tagged in this chapter.