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

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In summary, the person is having trouble finding the anti derivative of a function and has used two methods which have resulted in two different answers. They question whether the constant of 1/2 is an issue, but it is revealed that the two functions are actually the same and the only difference is in the constant. The person had incorrectly assumed that the two constants were the same.
  • #1
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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  • #2
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.
 

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

What is an anti derivative?

An anti derivative is the inverse operation of differentiation. It is a mathematical process used to find the original function when given its derivative.

What is the "Anti Derivative Issue: Is 1/2 Constant an Issue?"

This issue refers to the debate among mathematicians about whether or not the constant value of 1/2 should be included in the formula for anti derivatives.

Why is there a debate about the inclusion of 1/2 in anti derivative formulas?

The inclusion of 1/2 in anti derivative formulas can lead to inconsistencies and discrepancies in solving certain problems. Some mathematicians argue that it should be included for the sake of symmetry, while others argue that it should not be included to simplify calculations.

How does the inclusion of 1/2 affect the accuracy of anti derivative calculations?

The inclusion of 1/2 can lead to a difference of 1/2 in the final result of anti derivative calculations. While this may not seem significant, it can cause errors in more complex calculations.

What is the current consensus on the "Anti Derivative Issue: Is 1/2 Constant an Issue?"

There is still ongoing debate and discussion among mathematicians about the inclusion of 1/2 in anti derivative formulas. Some mathematicians choose to include it, while others do not. Ultimately, the choice depends on the specific problem being solved and the preferences of the mathematician.

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