BdMO National Higher Secondary 2008/4

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Moon
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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 \[\int_{0}^{1} f(x)dx\]
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nafistiham
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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 $IX-X$. :(
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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bristy1588
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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

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Tahmid Hasan
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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

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bristy1588
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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

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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.

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