This integral looks impossible...until you see this #integration #calculuswithij #cbseclass12
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This integral looks impossible...until you see this #integration #calculuswithij #cbseclass12
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YouTubeCalculus with IJ
This integral trick saves you time #calculuswithij #cbseclass12 #integration
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YouTubeCalculus with IJ
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🤔We solve the integral using algebraic manipulation #calculus #mathematics #integrals
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🔥 Day 107 — Can you solve this? Evaluate the integral: ∫ from 0 to ∞ of 1 / (1 x^2)^2 dx It looks messy — but one substitution makes it melt away 😮‍💨 Set x = tan θ and it turns into a simple cosine-square integral. 👉 The move: dx/(1 x^2)^2 → cos^2(θ) dθ with θ in [0, π/2]. Then integrate cos^2(θ) cleanly with a double-angle identity 👀 Would you land the exact value before time runs out? ⏱️ 💭 Drop your answer below 👇 ✅ Full step-by-step solution is already on my page. ➡️ Follow for Day 108
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🔥 Day 132 — 2025 MIT Integration Bee (Qualifying) Q16 Evaluate: ∫ [ sin(4x) * cos(x) ] / [ cos(2x) * sin(x) ] dx It looks nasty, but this one collapses fast. Expand sin(4x), cancel what you can, and the integrand turns into a simple power of cos. From there it’s a one-liner with the double-angle identity. 👉 Hints • sin(4x) = 2 sin(2x) cos(2x) = 4 sin x cos x cos(2x) • Most things cancel → 4 cos^2 x • Use cos^2 x = (1 cos 2x)/2 Would you spot the cancellations under time pressure? ⏱️ 💭 Comment
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