Integrals Class 12 Maths Notes – Formulas & Quick Revision

Integrals Class 12 ka sabse bada chapter hai — substitution, by parts, partial fractions aur definite integral properties. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Integrals

• ∫xⁿdx = xⁿ⁺¹/(n+1) + C
• ∫eˣdx = eˣ; ∫1/x dx = ln|x|
• ∫tanx dx = ln|secx|; ∫secx dx = ln|secx + tanx|
• ∫dx/(x²+a²) = (1/a)tan⁻¹(x/a)
• ∫dx/√(a²−x²) = sin⁻¹(x/a)
• By parts: ∫u·v dx = u∫v − ∫[u′∫v] (ILATE order)
• ∫eˣ[f(x) + f′(x)]dx = eˣf(x)
• Property: ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx

Quick Revision Points

• ILATE se u choose karo (Inverse, Log, Algebraic, Trig, Exponential)
• Partial fractions degree check karke lagao
• King property (f(a+b−x)) definite integrals ka sabse powerful tool hai
• Even/odd function properties se aadhe questions turant solve
• Standard forms pehchanna practice se aata hai — roz 5 integrals karo

FAQ

Integration approach kaise decide karu?

PDF mein method-selection flowchart hai — form dekho, method khud dikh jayega.

Definite integral properties kaunsi important?

King property + even/odd — boards ke 4-6 markers inhi se bante hain.

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