BdMO National Higher Secondary 2008/4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
User avatar
Moon
Site Admin
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Location: Dhaka, Bangladesh
Contact:

BdMO National Higher Secondary 2008/4

Unread post by Moon » Sun Feb 06, 2011 11:17 pm

Problem 4:
The function $f(x)$ is a complicated nonlinear function. It satisfies, $f(x) + f(1-x) = 1$. Evaluate \[\int_{0}^{1} f(x)dx\]
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

User avatar
nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

Re: BdMO National Higher Secondary 2008/4

Unread post by nafistiham » Tue Jan 10, 2012 6:34 pm

It was also a problem in the secondary.But we don't read this kind of functions in class $IX-X$. :(
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

User avatar
bristy1588
Posts: 92
Joined: Sun Jun 19, 2011 10:31 am

Re: BdMO National Higher Secondary 2008/4

Unread post by bristy1588 » Sat Jan 14, 2012 10:05 am

TIHAM,

Hint:
Use the following. It might help: :)

1.$\int_{a}^{b}f(g(x))d(g(x))=\int_{g(a)}^{g(b)}f(x)dx$

2.$\frac{d}{dx}(a-x)=-1$

$d(a-x)=-dx$
Answer:
$\frac{1}{2}$
Bristy Sikder

User avatar
Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm
Location: Khulna,Bangladesh.

Re: BdMO National Higher Secondary 2008/4

Unread post by Tahmid Hasan » Sat Jan 14, 2012 1:04 pm

আমি তেমন ক্যাল্কুলাস পারি না,তবে লেখ অঙ্কন করলে একটা ক্ষেত্রে প্রতিসাম্য পাওয়া যায় যা দিয়ে সহজে সমাধান সম্ভব।
উত্তর :$\frac {1}{2}$
বড় ভালবাসি তোমায়,মা

User avatar
bristy1588
Posts: 92
Joined: Sun Jun 19, 2011 10:31 am

Re: BdMO National Higher Secondary 2008/4

Unread post by bristy1588 » Sat Jan 14, 2012 1:11 pm

Tahmid, Tumi ki doye korso bolba??
Bristy Sikder

User avatar
samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

Re: BdMO National Higher Secondary 2008/4

Unread post by samiul_samin » Wed Feb 21, 2018 7:01 pm

This problem is discussed and solved here.

Post Reply