Definite Integration JEE Main PYQs PDF, 2020–2026

Definite Integration 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 223 of the 225 asked.

Topic-wise weightage by year

How many Definite Integration 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 31 JEE Main 2026 Definite Integration questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Properties of Definite Integrals

   Let $f(x)=\left\{\begin{array}{cc}\frac{1}{3}, & x\leq \pi/2 \\ \frac{{\ \mathrm{b}}(1-\sin x)}{(\pi-2x)^{2}}, & x>\pi/2\end{array}\right.$. If $f$ is continuous at $x=\pi/2$, then the value of $\int_{0}^{{3{\ \mathrm{b}}-6}}\left|x^{2}+2x-3\right|{\mathrm{d}}x$ is :

   Solve it online →

2. JEE Main 2026 · 8 Apr · Shift 2 · Properties of Definite Integrals

   If $\int_{{\pi/6}}^{{\pi/4}}\left(\cot \left(x-\frac{\pi}{3}\right)\cot \left(x+\frac{\pi}{3}\right)+1\right)dx=\alpha\log_{{{\mathrm{e}}}}(\sqrt{3}-1)$, then $9\alpha^{2}$ is equal to $\_\_\_\_$ .

   Solve it online →

3. JEE Main 2026 · 8 Apr · Shift 2 · Properties of Definite Integrals

   The value of the integral $\int_{0}^{2}\frac{\sqrt{x(x^{2}+x+1)}}{(\sqrt{x+1})\left(\sqrt{x^{4}+x^{2}+1}\right)}{\mathrm{d}}x$ is equal to:

   Solve it online →

4. JEE Main 2026 · 6 Apr · Shift 1 · Properties of Definite Integrals

   The value of the integral $\int_{{-\frac{\pi}{4}}}^{{\frac{\pi}{4}}}\left(\frac{32\cos^{4}x}{1+e^{{\sin x}}}\right)dx$ is :

   Solve it online →

5. JEE Main 2026 · 6 Apr · Shift 2 · Leibniz Rule

   Let ${\mathrm{A}}=\left[\begin{array}{ccc}1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1\end{array}\right]$ be a singular matrix. Let $f(x)=\int_{0}^{x}\left({\mathrm{t}}^{2}+2{\mathrm{t}}+3\right){\mathrm{dt}},x\in [1,\alpha]$. If M and m are respectively the maximum and the minimum values of $f$ in $[1,\alpha]$, then $3({\mathrm{M}}-{\mathrm{m}})$ is equal to :

   Solve it online →

6. JEE Main 2026 · 6 Apr · Shift 2 · Properties of Definite Integrals

   The value of the integral $\int_{{-1}}^{1}\left(\frac{x^{3}+|x|+1}{x^{2}+2|x|+1}\right){\mathrm{d}}x$ is equal to:

   Solve it online →

7. JEE Main 2026 · 5 Apr · Shift 2 · Properties of Definite Integrals

   Let $\left(2^{{1-{\mathrm{a}}}}+2^{{1+{\mathrm{a}}}}\right),f({\mathrm{a}}),(3^{{{\mathrm{a}}}}+3^{{-{\mathrm{a}}}})$ be in A.P. and $\alpha$ be the minimum value of $f({\mathrm{a}})$. Then the value of the integral $\int_{{\log_{e}(\alpha-1)}}^{{\log_{e}(\alpha)}}\frac{dx}{(e^{{2x}}-e^{{-2x}})}$ is :

   Solve it online →

8. JEE Main 2026 · 5 Apr · Shift 1 · Properties of Definite Integrals

   The value of the integral $\int_{{\frac{\pi}{6}}}^{{\frac{\pi}{3}}}\left(\frac{4-\operatorname{cosec}^{2}x}{\cos^{4}x}\right)dx$ is :

   Solve it online →

9. JEE Main 2026 · 5 Apr · Shift 1 · Properties of Definite Integrals

   The value of the integral $\int_{0}^{{\infty}}\frac{\log_{e}(x)}{x^{2}+4}dx$ is:

   Solve it online →

10. JEE Main 2026 · 4 Apr · Shift 2 · Properties of Definite Integrals

    If $\alpha=1$ and $\beta=1+i\sqrt{2}$, where $i=\sqrt{-1}$ are two roots of the equation

    $x^{3}+ax^{2}+bx+c=0,a,b,\in {\mathbb{R}}$, then $\int_{{-1}}^{1}\left(x^{3}+ax^{2}+bx+c\right)dx$ is equal to:

    Solve it online →

11. JEE Main 2026 · 4 Apr · Shift 2 · Properties of Definite Integrals

    The integral $\int_{0}^{1}\cot^{{-1}}\left(1+x+x^{2}\right)dx$ is equal to :

    Solve it online →

12. JEE Main 2026 · 4 Apr · Shift 1 · Properties of Definite Integrals

    Let $\int_{{-2}}^{2}(|\sin x|+[x\sin x])dx=2(3-\cos 2)+\beta$, where [ ⋅ ] is the greatest integer function. Then $\beta\sin \left(\frac{\beta}{2}\right)$ equals:

    Solve it online →

Practise the 2026 Definite Integration questions online

Sample questions from recent papers

The free PDF above has all 223 questions grouped by topic, with an answer key.

Frequently asked

More Mathematics chapters

• Applications of Derivatives (156 asked · 153 in PDF)
• Area Under Curves (138 asked · 136 in PDF)
• Binomial Theorem (197 asked · 196 in PDF)
• Circles (117 asked · all in PDF)
• Complex Numbers (162 asked · 161 in PDF)
• Continuity & Differentiability (94 asked · all in PDF)
• Determinants (188 asked · all in PDF)
• Differential Equations (204 asked · 202 in PDF)
• Differentiation (38 asked · all in PDF)
• Ellipse (100 asked · all in PDF)
• Functions (Advanced) (71 asked · all in PDF)
• Hyperbola (63 asked · 62 in PDF)
• Indefinite Integration (60 asked · all in PDF)
• Inverse Trigonometric Functions (94 asked · all in PDF)
• Limits (110 asked · all in PDF)
• Matrices (111 asked · all in PDF)
• Parabola (107 asked · 104 in PDF)
• Permutations & Combinations (163 asked · 162 in PDF)
• Probability: Advanced (97 asked · all in PDF)
• Probability: Basic (79 asked · 78 in PDF)
• Quadratic Equations & Polynomial Inequalities (129 asked · 128 in PDF)
• Relations & Functions (Basic) (139 asked · 137 in PDF)
• Sequences & Series (247 asked · 246 in PDF)
• Sets (39 asked · all in PDF)
• Statistics (104 asked · all in PDF)
• Straight Lines (130 asked · 123 in PDF)
• Three Dimensional Geometry (297 asked · all in PDF)
• Trigonometric Equations (48 asked · all in PDF)
• Trigonometric Ratios & Identities (85 asked · 63 in PDF)
• Vectors (216 asked · 212 in PDF)

JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020