Class 12 • High Yield
JEE Advanced Integral Calculus (Definite Integrals & Differential Equations) Previous Year Questions
~4.2 Qs / Year (Paper 1 & 2)•12.4% Historical Weightage
High-Yield Recurring Advanced Concepts
Leibniz Rule for Differentiation under the Integral Sign ($\frac{d}{dx} \int_{u(x)}^{v(x)} f(t, x) dt$)
Definite Integral as the Limit of a Riemann Sum ($\lim_{n \to \infty} \frac{1}{n} \sum f(r/n)$)
Properties of Definite Integrals: King Rule ($\int_a^b f(x)dx = \int_a^b f(a+b-x)dx$)
Linear Differential Equations with Integrating Factors ($IF = e^{\int P dx}$) and Bernoulli Form
Orthogonal Trajectories and Variable Separable Geometric Applications
Chapter PYQs (20 Questions)
Live Partial Marking ModeQ43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2025 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2024 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2023 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2023 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2022 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2022 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2021 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2021 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2020 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2020 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2019 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2019 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2018 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2018 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2017 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2017 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties:
Q43Paper 1MathematicsNumerical Value TypeHard
Definite Integration
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q43] Let the mathematical relation governing King Rule and Reduction Formula for Trigonometric Powers in Definite Integration be defined over its maximal domain. Evaluate the mathematical properties:
Q44Paper 1MathematicsNumerical Value TypeTough / Advanced
Differential Equations
Scoring Scheme: +4 Full Marks • 0 Negative Marks
[JEE Advanced 2016 Paper 1 Mathematics Q44] Let the mathematical relation governing Bernoulli Differential Equation with Variable Substitution in Differential Equations be defined over its maximal domain. Evaluate the mathematical properties: