JEE Main Integration Shortcut — Definite Integrals Made Easy 💡
❓ Concept Integration Trick – tan⁻¹ Form in 60 Sec! Whenever you see an integral of the type ∫ sin x a + b cos 2 x d x (or with extra terms in the numerator), understand one thing clearly 👇 👉 This is a pure tan⁻¹ game . ✍️ Short Explanation This type of integral is very common in JEE Main + Advanced . The key idea is: sin x dx is the derivative of cos x The denominator becomes a quadratic in cos x Final answer always involves tan⁻¹ 1️⃣ Step 1 — Identify the Pattern Integral of the form: ∫ (something) ⋅ sin x a + b cos 2 x d x 👉 Always try substitution : u = cos x u = \cos x d u = − sin x d x du = -\sin x\,dx This instantly simplifies the integral. 2️⃣ Step 2 — Apply Substitution From substitution: sin x d x = − d u \sin x\,dx = -du For definite integrals , limits change: x = 0 ⇒ u = cos 0 = 1 x = 0 \Rightarrow u = \cos 0 = 1 x = π ⇒ u = cos π = − 1 x = \pi \Rightarrow u = \cos \pi = -1 So the integral converts into: ...
