Anti Derivative Issue: Is 1/2 Constant an Issue?

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SUMMARY

The discussion centers on the anti-derivative of a function where two methods yield different constants, specifically a constant of 1/2. The participants conclude that despite the differing constants, both results represent the same function after applying the initial condition. The key takeaway is that the constants of integration (C) can differ, but they do not affect the overall function when initial conditions are applied.

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gruveb
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I have a slight problem taking the anti derivative of a function. Using two methods I get two answers. Look at the picture to see the difference.

I think that they're both the same, but one has a constant of 1/2. Is this an issue?
http://hphotos-snc3.fbcdn.net/hs413.snc3/24919_1290260109877_1631487092_714376_3645281_n.jpg
 
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They're the same. Notice that the only difference in those two is (1/2) (look at the bottom right). However, the C attributes for this difference. The Cs are different in both of these functions, but after applying the initial condition, you will get the exact same function. You were assuming that the two Cs were the same.
 

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