Area Under Curves — JEE Main PYQs & Practice Questions

Area Under Curves is a Mathematics chapter in the JEE Main syllabus. This page brings together 136 previous-year and practice questions on Area Under Curves, organised into 3 topics: Area Between Curve and Axis, Area Between Two Curves and Area of Standard Regions. Most questions come with a step-by-step solution you can work through free in PrepWiser.

Download Area Under Curves JEE Main PYQs as a free PDF (with answer key)

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Chapter weightage: how many questions each chapter had per shift in the 2024–26 papers.

Area Between Curve and Axis

• Let f: R → R be a twice differentiable function such that f(x+y)=f(x) f(y) for all x, y…

Area Between Two Curves

• If the area of the region {(x,y):|x²-2|≤ y≤ x} is A, then 6A+16√2 is equal to __________.
• If the area of the larger portion bounded between the curves x²+y²=25 and y=|x-1| is…
• The area, enclosed by the curves y=sin x+cos x and y=|cos x-sin x| and the lines…
• Let e be the base of natural logarithm and let f:{1,2,3,4}→ {1,e,e²,e³} and…
• Let A be the area bounded by the curve y=x|x-3|, the x-axis and the ordinates x=-1 and…
• The area of the region bounded by y² = 8x and y² = 16(3 - x) is equal to:
• If the area of the region {(x,y):0≤ y≤ min{2x,6x-x²}} is A, then 12 A is equal to…
• The area of the region, inside the ellipse x²+4y²=4 and outside the region bounded by…
• The area of the region bounded by the curve y=max{|x|,x|x-2|}, the x-axis and the lines…
• The area of the region {(x,y):x²≤ y≤ |x²-4|,y≥ 1} is
• The area of the region {(x,y):|x-y|≤ y≤ 4√x} is
• Three points O(0,0),P(a,a²),Q(-b,b²),a>0, b>0, are on the parabola y=x². Let S₁ be the…
• The parabola y²=4x divides the area of the circle x²+y²=5 in two parts. The area of the…
• Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve…
• The area of the region {(x,y):0≤ y≤ 6-x,y²≥ 4x-3,x≥ 0} is :
• If the area of the region {(x,y):1-2x≤ y≤ 4-x², x≥ 0, y≥ 0} is α/β, α,β∈ ℕ,gcd(α,β)=1…
• The area of the region enclosed by y≤ 4x²,x²≤ 9y and y≤ 4, is equal to :
• The area of the region S = (x, y) : y² ≤ 8x, y ≥ √2x, x ≥ 1 is
• The area of the smaller region enclosed by the curves y²=8x+4 and x²+y²+4√3x-4=0 is…
• If the area of the region {(x,y):1+x²≤ y≤ min{x+7,11-3x}} is A, then 3A is equal to :

Area of Standard Regions

• The area bounded by the curve 4y² = x²(4 - x)(x - 2) is equal to :
• The area of the bounded region enclosed by the curve y=3-|x-1/2|-|x+1| and the x-axis is :
• Let A₁ be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in…
• If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = 3/2 and the…

More Mathematics chapters

• Sets
• Relations & Functions (Basic)
• Trigonometric Ratios & Identities
• Trigonometric Equations
• Inverse Trigonometric Functions
• Properties of Triangles
• Complex Numbers
• Quadratic Equations & Polynomial Inequalities
• Sequences & Series
• Binomial Theorem
• Permutations & Combinations
• Mathematical Induction
• Statistics
• Probability — Basic
• Straight Lines
• Circles
• Parabola
• Ellipse
• Hyperbola
• Limits
• Continuity & Differentiability
• Differentiation
• Applications of Derivatives
• Indefinite Integration
• Definite Integration
• Differential Equations
• Vectors
• Three Dimensional Geometry
• Matrices
• Determinants
• Functions (Advanced)
• Probability — Advanced

Frequently asked questions

How many Area Under Curves questions are there for JEE Main?

PrepWiser has 136 Area Under Curves questions for JEE Main, grouped into 3 topics such as Area Between Curve and Axis, Area Between Two Curves and Area of Standard Regions.

Are these Area Under Curves questions from previous-year JEE Main papers?

Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.

Where can I see the answers and solutions to these Area Under Curves questions?

Open any Area Under Curves question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.