nice integral
by Martin.s, May 27, 2025, 5:13 PM
![\[
\int_{0}^{1} \frac{dx}{(\ln x + i\pi)^2\,(1 - x + e^{i\pi})}
\]](http://latex.artofproblemsolving.com/2/7/d/27d389a41148543ea478644e4bc6e0a1258f0d04.png)
Evaluate: $\int_{0}^{\pi} \text{min}\{2\sin x,1-\cos x,1\} dx$
by Vulch, May 27, 2025, 9:11 AM
Evaluate: 
Evaluate: $\int_{-1}^{1} \text{max}\{2-x,2,1+x\} dx$
by Vulch, May 27, 2025, 9:08 AM
Evaluate: 
This post has been edited 1 time. Last edited by Vulch, Yesterday at 9:11 AM
Infinite Sum
by P162008, May 27, 2025, 6:18 AM
Let 
be the nearest integer to 
.
Find the value of
Also, generalise your result.
be the nearest integer to 
.Find the value of
Also, generalise your result.Sequence and Series
by P162008, May 27, 2025, 6:12 AM
Given the sequence 
such that 
and 
. Find the value of 
such that 
and 
. Find the value of 
IMC 2009 Day 1 P2
by joybangla, Jul 15, 2014, 3:20 PM
Let 
be real square matrices of the same order, and suppose 
is invertible. Prove that
![\[ (A-B)C=BA^{-1}\implies C(A-B)=A^{-1}B \]](//latex.artofproblemsolving.com/0/6/0/06007271017c2c48faa708366f1adc67db91f245.png)
be real square matrices of the same order, and suppose 
is invertible. Prove that![\[ (A-B)C=BA^{-1}\implies C(A-B)=A^{-1}B \]](http://latex.artofproblemsolving.com/0/6/0/06007271017c2c48faa708366f1adc67db91f245.png)
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