am i missing something in my simplifying?

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lethalasian

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So I am doing integrals but i have a simplifying question. After integrating I am left with ((x+2)^3)/3 - x^3/3
The solution when simplifying got the result 2x(x+2) however that is not what I got.
I just want to know if anyone can see how they got there.
 
I think I'd factor out the 1/3 and expand the cube:

[MATH]\frac{1}{3}(x^3+6x^2+12x+8-x^3)[/MATH]
Combine like terms
'
[MATH]\frac{1}{3}(6x^2+12x+8)[/MATH]
Factor out 2:

[MATH]\frac{2}{3}(3x^2+6x+4)[/MATH]
 
I'm guessing that you have a solution given? It's hard to say where you might have gone wrong if we can't see your work!

Hint:
[math]\dfrac{(x + 2)^3}{3} - \dfrac{x^3}{3} = \dfrac{1}{3} ( (x + 2)^3 - x^3 )[/math].

So what's [math](x + 2)^3 - x^3[/math]
-Dan
 
[MATH]\dfrac{(x^3 + 2)^3}{3} - \dfrac{x^3}{3} = \dfrac{x^3 + 3x^2 * 2 + 3x * 2^2 + 2^3 - x^3}{3} = \dfrac{6x^2 + 12x + 8}{3} = 2x(x +2) + \dfrac{8}{3}.[/MATH]
So either your answer key has a typo, or you made an error in integration. We can't tell you which is correct because you told us nothing about the problem in integration.
 
Last edited:
Don't forget the arbitrary constant! That is a common reason for confusion over simplified answers that look different!

Your answer is, as you've been shown, 2x(x+2) + 8/3 + C. But since C is arbitrary (that is, it can be any number), you can write the answer just as 2x(x+2) + C, where this C is just 8/3 more than your C.

There is no typo. But, yes, showing the entire problem would have helped us realize that quicker.
 
JeffM and OP,
I assume that this was an indefinite integral.
So both solutions posted are wrong! They should both have a +C at the end!
Now assuming that Jeff did his calculation correct, and I am sure he did as Jeff never makes any mistakes, than your solution and the textbook solution differ by a constant which is perfectly fine.

Do you understand why?
 
Dr P, i just read the post and within seconds wrote my reply. How can you read my mind? Can you please stop plagiarism?!
 
Sorry. I'll try to ignore those signals I get from your brain implant, or at least hold off a few minutes.

I won't say great minds think alike. (Even mediocre minds think alike when they're right.)
 
@Dr.Peterson Thank you I just read over it again and your answer is right!
The C is arbitrary because when plugging in the limits it can be just subtracted from itself. So the answer is 2x(x+2)

Sorry for the confusion but thank you for everyone that answered
 
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