Indefinite Integral Confusion

[RandallJ]

Hello SFN,

 

I am an occasional lurker who has a question.

Well, more or less an inconsistency.

 

This problem was something along the lines of :

 

 

Find the anti-derivative of (2x + 1)^3. and the inital value if g(1) = 100

 

 

The anti-derivative should be :

 

((2x + 1)^4) / 8 + c

 

And c would come out to be 89.875.

 

I assume we could expand (2x+1)^3 to 8x^3 + 12x^2 + 6x + 1 and proceed to find the anti-derivative, 2x^4 + 4x^3 + 3x^2 + x + c. If we use g(1) = 100, you come up with c = 90.

 

My question is : where is the 1/8 difference coming from?

 

 

Thanks for your help,

RandallJ

[Bignose]

The difference is that you already have part of a constant in ( (2x+1)^4 )/8.

 

If you expand that out, you get:

 

2x^4 + 4x^3 + 3x^2 + x + (1/8) <---- and there is your missing (1/8)

 

It is subtle difference you have uncovered between definite and indefinite integrals, however, it is important to note that in the end you still got the exact same result. In the first function, the sum of the two constants is the same as the constant you got in the second, so it all came out the same in the end.

[RandallJ]

Thank you very much Bignose!

 

That was really killing me.