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A beautiful integral with a beautiful result! #maths #calculus #integral #engineering
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🧠 Reactivo #68 Matemáticas – Guía UNAM 2026 Esta integral de la guía UNAM 2026 parece difícil, pero en realidad es de las más fáciles del examen 📚 Tenemos que calcular: ∫ cos(8x) dx Sabemos que: ∫ cos(x) dx = sen(x) C Pero cuando aparece ax dentro del coseno, usamos la regla: ∫ cos(ax) dx = (1/a) sen(ax) C Aquí a = 8, entonces: (1/8) sen(8x) C También se puede escribir como: sen(8x) / 8 C Respuesta correcta: sen(8x) / 8 C — inciso D ✅ 📘 Domina Matemáticas y todas las materias del examen a la
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🔥 Day 117 — Can you solve this? Evaluate the integral (a > 0, b ≥ 0): ∫₀^∞ e^(−a x) · sin(bx) / x dx It looks tough — but a parameter derivative makes it collapse 📉 Differentiate with respect to b, use the Laplace transform of cos(bx), then integrate back. 👉 Hint: F′(b) = ∫₀^∞ e^(−a x) cos(bx) dx = a/(a² b²). Integrate in b and use F(0) = 0 to nail the constant 👀 Would you land the exact expression before time runs out? ⏱️ 💭 Drop your answer below 👇 ✅ Full step-by-step solution is already
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TikTokbrainrot.mathematics
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