Page 1 of 1
BdMO National 2008: Secondary
Posted: Mon Dec 19, 2016 9:01 pm
by Kazi_Zareer
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 2008: Secondary
Posted: Fri Jan 13, 2017 6:37 pm
by ahmedittihad
Is that a deriviative sign?
Re: BdMO National 2008: Secondary
Posted: Fri Jan 13, 2017 10:44 pm
by Thanic Nur Samin
ahmedittihad wrote:Is that a deriviative sign?
That is a integreation sign.
$$\displaystyle \int_0^1f(x)dx=\dfrac{1}{2}\left(\int_0^1f(x)dx+\int_0^1f(1-x)dx\right)$$
$$\displaystyle =\dfrac{1}{2}\left(\int_0^1(f(x)+f(1-x))dx\right)$$
$$\displaystyle =\dfrac{1}{2}\int_0^1 dx=\dfrac{1}{2}$$
Re: BdMO National 2008: Secondary
Posted: Sat Jan 14, 2017 12:46 pm
by ahmedittihad
Do we need calculus in Math Olympiads?!
Re: BdMO National 2008: Secondary
Posted: Sat Jan 14, 2017 1:42 pm
by Thanic Nur Samin
I think not. This problem just used the very basics. I can't say anything about the nationals, but in IMO, APMO and other contests, you won't need it.
Re: BdMO National 2008: Secondary
Posted: Wed Feb 21, 2018 6:59 pm
by samiul_samin
A particular formula kills the problem