Distribution function primitive

[cham]

Homework Statement

the distribution function: f(x)=
x + 1 when -1 < x ≤ 0
-x + 1 when 0 ≤ x < 1
0 otherwise

Homework Equations

The Attempt at a Solution

on the first interval i found (1/2)x² +x + c
on the second interval -(1/2)x² + x + c
and when integrating the c's will cancel each other

now my math teacher found
on the first inervall f= (1/2)x² +x+1/2
on the second f=-(1/2)x² + x +1/2
f=1 otherwise

now i want to know how did find that c=1/2 because we have to draw the graph

 

[haruspex]

It's not clearly stated, but I gather you are trying to find the cumulative distribution function from the density function. ('Distribution function' is not specific enough.)
Why do you say the c's cancel? Using the CDF you found for the second interval, including the unknown c, what does that tell you about the CDF at +infinity? What value must a CDF take at +infinity?

 

[Ray Vickson]

Homework Statement

the distribution function: f(x)=
x + 1 when -1 < x ≤ 0
-x + 1 when 0 ≤ x < 1
0 otherwise

Homework Equations

The Attempt at a Solution

on the first interval i found (1/2)x² +x + c
on the second interval -(1/2)x² + x + c
and when integrating the c's will cancel each other

now my math teacher found
on the first inervall f= (1/2)x² +x+1/2
on the second f=-(1/2)x² + x +1/2
f=1 otherwise

now i want to know how did find that c=1/2 because we have to draw the graph

Please do not use boldface font for the whole message---only for parts you really want to emphasize (as I do below).
Mod note: I removed the excess boldface.
Anyway: you need F(-1) = 0 and F(1) = 1, so that tells you what must be the value of c.

Note: do NOT use the same letter, f, for both the density function and the distribution function; your second function should be called F, or at least by some other symbol different from your first f. Using the same symbol for two different quantities in the same problem is a sure way to lose marks for no good reason!