Area Under Curves JEE Main PYQs PDF, 2020–2026

Area Under Curves questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 136 of the 138 asked.

Topic-wise weightage by year

How many Area Under Curves questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 19 JEE Main 2026 Area Under Curves questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Area Between Two Curves

   Let $f:(1,\infty)\rightarrow {\mathbf{R}}$ be a function defined as $f(x)=\frac{x-1}{x+1}$. Let $f^{{i+1}}(x)=f\left(f^{i}(x)\right),i=1,2,\ldots,25$, where $f^{1}(x)=f(x)$. If $g(x)+f^{{26}}(x)=0,x\in (1,\infty)$, then the area of the region bounded by the curves $y=g(x),2y=2x-3,y=0$ and $x=4$ is :

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2. JEE Main 2026 · 6 Apr · Shift 1 · Area Between Two Curves

   Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\rightarrow \left\{1,e,e^{2},e^{3}\right\}$ and ${\mathrm{g}}:\left\{1,e,e^{2},e^{3}\right\}\rightarrow \left\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4}\right\}$ be two bijective functions such that $f$ is strictly decreasing and $g$ is strictly increasing. If $\phi(x)=\left[f^{{-1}}\left\{g^{{-1}}\left(\frac{1}{2}\right)\right\}\right]^{x}$, then the area of the region ${\mathrm{R}}=\left\{(x,y):x^{2}\leq y\leq \phi(x),0\leq x\leq 1\right\}$ is :

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3. JEE Main 2026 · 6 Apr · Shift 1 · Area Between Two Curves

   The area of the region $\left\{(x,y):0\leq y\leq 6-x,y^{2}\geq 4x-3,x\geq 0\right\}$ is :

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4. JEE Main 2026 · 6 Apr · Shift 2 · Area Between Two Curves

   The area of the region $\left\{(x,y):x^{2}-8x\leq y\leq -x\right\}$ is :

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5. JEE Main 2026 · 5 Apr · Shift 1 · Area Between Two Curves

   The area of the region ${\mathrm{R}}=\left\{(x,y):xy\leq 27,1\leq y\leq x^{2}\right\}$ is equal to :

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6. JEE Main 2026 · 5 Apr · Shift 2 · Area Between Two Curves

   Let $f:{\mathbf{R}}\rightarrow {\mathbf{R}}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x,x\in {\mathbf{R}}$. Let the maximum value of $f$ on ${\mathbf{R}}$ be $\alpha$. If the area of the region bounded by the curves $g(x)=x^{2}$ and $h(x)=\beta x^{3},\beta>0$, is $\alpha^{2}$, then $30\beta^{3}$ is equal to $\_\_\_\_$ .

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7. JEE Main 2026 · 4 Apr · Shift 2 · Area Between Two Curves

   The area of the region bounded by the curves $x+3y^{2}=0$ and $x+4y^{2}=1$ is equal to :

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8. JEE Main 2026 · 4 Apr · Shift 1 · Area Between Two Curves

   The area of the region $\{(x,y):y\leq \pi-|x|,y\leq |x\sin x|,y\geq 0\}$ is:

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9. JEE Main 2026 · 2 Apr · Shift 2 · Area Between Two Curves

   If the area of the region bounded by $16x^{2}-9y^{2}=144$ and $8x-3y=24$ is $A$, then $3(A+6\log_{e}(3))$ is equal to ________.

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10. JEE Main 2026 · 28 Jan · Shift 2 · Area Between Two Curves

    Let $P_{1}:y=4x^{2}$ and $P_{2}:y=x^{2}+27$ be two parabolas. If the area of the bounded region enclosed between $P_{1}$ and $P_{2}$ is six times the area of the bounded region enclosed between the line $y=\alpha x$, $\alpha>0$ and $P_{1}$, then $\alpha$ is equal to :

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11. JEE Main 2026 · 28 Jan · Shift 1 · Area Between Two Curves

    The area of the region ${\mathrm{R}}=\left\{(x,y):xy\leq 8,1\leq y\leq x^{2},x\geq 0\right\}$ is

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12. JEE Main 2026 · 24 Jan · Shift 2 · Area Between Two Curves

    Let $f(\alpha)$ denote the area of the region in the first quadrant bounded by $x=0,x=1,y^{2}=x$ and $y=|\alpha x-5|-|1-\alpha x|+\alpha x^{2}$. Then $(f(0)+f(1))$ is equal to

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Practise the 2026 Area Under Curves questions online

Sample questions from recent papers

The free PDF above has all 136 questions grouped by topic, with an answer key.

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