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Hey=)
Sorry to disturb you but I have this really difficult question that I just cant figure out:
The curves shown are all examples of graphs of continuous functions f on [0, 1] that have the following three properties:
(I) The endpoints lie on the x-axis:f(0)=0, f(0)=1
(II) The functions are non-negative:f(x)greater than or equal to 0 for x is greater than or equal to 0, x is greater than or equal to one
(III) The area under the graph of f from 0 to 1 is equal to 1
The lengths L of these curves, however, are different.
1)Find the formulae for two functions that satisfy all three of the properties (I), (II) and (III) given above.
Explain how you found your functions.
Ive been trying to work out this question for ages but couldnt work it out so if you could give me a hand I'd really appreciate it=)
Thank you
Hello Dil,
Here are 2 functions that satisfy the above :
1. f(x)=6x(1-x)
2. f(x)=(π/2)sin(πx)
You need to chick that :
a) f(x)=0 --> x1=0 %26 x2=1
b) for all 0≤x≤1 , f(x)≥0
1
c) ∫ f(x)dx = 1
0
I'll leave it to you to perform the check .
Alon.
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Alon Mandes
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