Jump to a section

Mathematics - Area Under Curves

Practise 20 JEE Advanced previous year questions on Area Under Curves, compiled from papers spanning 2008 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Area Under Curves has been asked in 17 of the 27 years of JEE Advanced papers analysed (2000–2026), with 20 questions in all. 15% of them were easy, 40% moderate and 45% tough. Most of its questions came from 2026, with 2 questions that year. In the last three years (2024–2026) it had 4 questions across 6 papers, about 0.7 per paper.

The chapter's 3 topics are not weighted equally: Area bounded by Miscellaneous Curves (9 questions, 45%), Area bounded by two curves (9 questions, 45%), and Area of Curve along axis (2 questions, 10%) have been asked the most. Over the last five years the most frequent topics have been Area bounded by two curves (4), Area bounded by Miscellaneous Curves (2), and Area of Curve along axis (1). Area bounded by Miscellaneous Curves has produced the most tough questions (5).

  1. 1Passage: Consider the curve given by for , and the curve given by for . Let be the total number of points of intersection of the curves and 2026 (Paper 2)Area bounded by two curves
  2. 2Passage: Consider the ellipses given by and . Question: If is the area of the common region that lies inside both the given ellipses, then t2026 (Paper 2)Area bounded by two curves
  3. 3Let denote the set of all real numbers. Then the area of the region is2025 (Paper 2)Area bounded by two curves
  4. 4Let and . If the area of the region is , then is equal to2024 (Paper 2)Area bounded by Miscellaneous Curves
  5. 5Let f : 0 , 1 0 , 1 be the function defined by f x = x 3 3 - x 2 + 5 9 x + 17 36 . Consider the square region S = 0 , 1 0 , 1 . Let G = x , 2023 (Paper 1)Area bounded by two curves
  6. 6Let n 2 be a natural number and f : 0 , 1 be the function defined by f x = n 1 - 2 n x if 0 x 1 2 n 2 n 2 n x - 1 if 1 2 n x 3 4 n 4 n 1 - n2023 (Paper 1)Area of Curve along axis
  7. 7Consider the functions f , g : defined by f x = x 2 + 5 12 and g x = 2 1 - 4 x 3 , x 3 4 , 0 , x 3 4 If is the area of the region x , y : x 2022 (Paper 2)Area bounded by Miscellaneous Curves
  8. 8The area of the region ( x , y ) : 0 x 9 4 , 0 y 1 , x 3 y , x + y 2 is2021 (Paper 1)Area bounded by Miscellaneous Curves
  9. 9Let the functions f : R R and g : R R be defined by f x = e x 1 e x 1 and g x = 1 2 e x 1 + e 1 x . Then the area of the region in the first2020 (Paper 1)Area bounded by Miscellaneous Curves
  10. 10The area of the region x , y : x y 8 , 1 y x 2 is2019 (Paper 1)Area bounded by two curves
  11. 11A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring 2018 (Paper 1)Area bounded by two curves
  12. 12If the line x = divides the area of the region R = { x , y R 2 : x 3 y x , 0 x 1 } into two equal parts, then2017 (Paper 2)Area bounded by two curves
  13. 13Area of the region { x , y R 2 : y x + 3 , 5 y x + 9 15 } is equal to2016 (Paper 2)Area bounded by two curves
  14. 14The area enclosed by the curves y = sin x + cos x and y = cos x - sin x over the interval 0 , 2 is2013 (Paper 1)Area bounded by two curves
  15. 15Let be the area of the region enclosed by , and ; then2012 (Paper 1)Area bounded by Miscellaneous Curves
  16. 16Let the straight line divide the area enclosed by and into two parts and such that . Then, equals to2011 (Paper 1)Area of Curve along axis
  17. 17Paragraph: Consider the polynomial . Let be the sum of all distinct real roots of and let . Question: The area bounded by the curve and the 2010 (Paper 2)Area bounded by Miscellaneous Curves
  18. 18Area of the region bounded by the curve and lines and is2009 (Paper 1)Area bounded by Miscellaneous Curves
  19. 19Paragraph: Consider the functions defined implicitly by the equation on various intervals in the real line. If , the equation implicitly def2008 (Paper 1)Area bounded by Miscellaneous Curves
  20. 20The area of the region between the curves and bounded by the lines and is2008 (Paper 2)Area bounded by Miscellaneous Curves

Frequently Asked Questions

1.How many questions are available for Area Under Curves?

This chapter includes 20 questions compiled from JEE Advanced papers spanning 2008 to 2026.

2.Are these questions only from JEE Advanced, or from other exams too?

These are JEE Advanced questions specifically for the Area Under Curves chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Area Under Curves an important chapter for JEE Advanced Mathematics?

Area Under Curves has appeared in 17 of the 21 years of JEE Advanced papers covered here, with 20 questions across 18 papers - about one per paper it appears in.

4.What is the difficulty level of Area Under Curves questions in JEE Advanced?

Of the 20 questions analysed for this chapter, 15% are easy, 40% moderate and 45% tough. 2026 had the most, with 2 questions.

5.Which topics in Area Under Curves should I focus on?

These topics have carried the most weightage in Area Under Curves:

  • Area bounded by Miscellaneous Curves - 9 questions (45%)
  • Area bounded by two curves - 9 questions (45%)
  • Area of Curve along axis - 2 questions (10%)
  • Area bounded by Miscellaneous Curves has produced the most tough questions (5).
6.Is Area Under Curves's weightage in JEE Advanced going up or down?

Across all 18 papers analysed, Area Under Curves has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.