BdMO National 2008: Secondary
- Kazi_Zareer
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The function $f (x) $ is a complicated nonlinear function. It satisfies, $ f(x) + f(1-x) = 1 $ . Evaluate $ \int_{0}^{1} f(x)dx $.
We cannot solve our problems with the same thinking we used when we create them.
- ahmedittihad
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- Thanic Nur Samin
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Re: BdMO National 2008: Secondary
That is a integreation sign.ahmedittihad wrote:Is that a deriviative sign?
$$\displaystyle \int_0^1f(x)dx=\dfrac{1}{2}\left(\int_0^1f(x)dx+\int_0^1f(1-x)dx\right)$$
$$\displaystyle =\dfrac{1}{2}\left(\int_0^1(f(x)+f(1-x))dx\right)$$
$$\displaystyle =\dfrac{1}{2}\int_0^1 dx=\dfrac{1}{2}$$
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
- ahmedittihad
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Re: BdMO National 2008: Secondary
Do we need calculus in Math Olympiads?!
Frankly, my dear, I don't give a damn.
- Thanic Nur Samin
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Re: BdMO National 2008: Secondary
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.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
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Re: BdMO National 2008: Secondary
A particular formula kills the problem