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BdMO National Higher Secondary 2008/4
Posted: Sun Feb 06, 2011 11:17 pm
by Moon
Problem 4:
The function $f(x)$ is a complicated nonlinear function. It satisfies, $f(x) + f(1-x) = 1$. Evaluate \[\int_{0}^{1} f(x)dx\]
Re: BdMO National Higher Secondary 2008/4
Posted: Tue Jan 10, 2012 6:34 pm
by nafistiham
It was also a problem in the secondary.But we don't read this kind of functions in class $IX-X$.
Re: BdMO National Higher Secondary 2008/4
Posted: Sat Jan 14, 2012 10:05 am
by bristy1588
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:
Re: BdMO National Higher Secondary 2008/4
Posted: Sat Jan 14, 2012 1:04 pm
by Tahmid Hasan
আমি তেমন ক্যাল্কুলাস পারি না,তবে লেখ অঙ্কন করলে একটা ক্ষেত্রে প্রতিসাম্য পাওয়া যায় যা দিয়ে সহজে সমাধান সম্ভব।
উত্তর :$\frac {1}{2}$
Re: BdMO National Higher Secondary 2008/4
Posted: Sat Jan 14, 2012 1:11 pm
by bristy1588
Tahmid, Tumi ki doye korso bolba??
Re: BdMO National Higher Secondary 2008/4
Posted: Wed Feb 21, 2018 7:01 pm
by samiul_samin
This problem is discussed and solved
here.