Olympiad problems

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Found problems: 28

2019 CMI B.Sc. Entrance Exam, 3

Tags: definite integral , recursion of integrals , algebra

Evaluate $\int_{ 0 }^{ \infty } ( 1 + x^2 )^{-( m + 1 )} \mathrm{d}x$ where $m \in \mathbb{N} $

Tags: calculus , integration , trigonometry , calculus computations , definite integral

Evaluate $\int_{-\pi}^{\pi} \left(\sum_{k=1}^{2013} \sin kx\right)^2dx$.

Tags: calculus , integration , trigonometry , calculus computations , definite integral , logarithm

Evaluate $\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{2+\sin x}{1+\cos x}\ dx.$