## BdMO National 2008: Secondary

Kazi_Zareer
Posts: 86
Joined: Thu Aug 20, 2015 7:11 pm
Location: Malibagh,Dhaka-1217

### BdMO National 2008: Secondary

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.

Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

### Re: BdMO National 2008: Secondary

Is that a deriviative sign?
Frankly, my dear, I don't give a damn.

Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am

### Re: BdMO National 2008: Secondary

ahmedittihad wrote:Is that a deriviative sign?
That is a integreation sign.

$$\displaystyle \int_0^1f(x)dx=\dfrac{1}{2}\left(\int_0^1f(x)dx+\int_0^1f(1-x)dx\right)$$

$$\displaystyle =\dfrac{1}{2}\left(\int_0^1(f(x)+f(1-x))dx\right)$$

$$\displaystyle =\dfrac{1}{2}\int_0^1 dx=\dfrac{1}{2}$$
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

### Re: BdMO National 2008: Secondary

Do we need calculus in Math Olympiads?!
Frankly, my dear, I don't give a damn.

Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am

### 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.

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

### Re: BdMO National 2008: Secondary

A particular formula kills the problem