Looks Impossible… But Collapses Beautifully! | JEE Advanced Maths
Автор: Factorial Academy
Загружено: 2026-02-16
Просмотров: 1953
Описание:
Looks Impossible… But Collapses Beautifully! | JEE Advanced Maths
In today’s Factorial’s Question of the Day, we discuss a beautiful JEE Advanced level integral that looks complicated but unlocks instantly once you recognise the hidden structure.
Before solving the main problem, we build the required prerequisite idea. This is exactly how advanced problems should be approached: understand the mechanism, not memorise tricks.
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✅ Question Discussed
Let
f(x,n)=\int \frac{x^2+n(n-1)}{(x\sin x+n\cos x)^2}\,dx,
where n\in\mathbb{N}.
It is given that
f(0,n)=0 \quad \text{for all } n\in\mathbb{N}.
Find the numerical value of
(12+\pi)\,f\!\left(\frac{\pi}{4},\,3\right).
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This problem is a perfect example of how JEE Advanced tests insight, not expansion.
If you enjoyed this, you must follow the entire Factorial’s Question of the Day series to sharpen your mathematical vision daily.
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