JEE Main Calculus: Complete Guide to Integration, Differentiation & DEs
Calculus is the highest-weightage topic in JEE Main Mathematics with 8-9 questions. Mastering Calculus can add 30-35 marks to your Maths score alone. Here is a systematic approach to each calculus chapter.
Limits and Continuity (2 questions)
Key techniques: Standard limits (sin x/x → 1, (1+1/n)^n → e), L'Hôpital's Rule, Squeeze theorem for IVT. Practice: 0/0 and ∞/∞ forms. JEE Main likes: limits involving trigonometric + polynomial combinations.
Differentiation (1-2 questions)
Beyond basic rules: Implicit differentiation, Higher-order derivatives, Parametric differentiation. Application questions: Maxima/Minima, Tangent/Normal equations, Mean Value Theorem. Rate of change problems appear as NVQs.
Integration (3-4 questions)
This is where most Maths marks live. Priority: Substitution, Integration by Parts, Partial Fractions, Definite integral properties (King's property especially). Learn: ∫₀^π x·f(sin x)dx = π/2 ∫₀^π f(sin x)dx — this appears every 2 years.
Differential Equations (1-2 questions)
JEE Main focuses on: Variable Separable, Homogeneous DEs, Linear first-order DEs (integrating factor). Applications: Population growth, cooling problems. Degree and order of a DE is often a direct 1-mark question.
Calculus Fast Track Tips
Learn 50 standard integration results by heart. Practice 5 integration questions daily. For DEs, always identify the type first before solving. Use differentiation under integral sign for complex definite integrals.
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