## Different methods of Integration for addition, results differ?

Ignore, I worked it out. Was a simple mistake on my part.

A very simple integration of ∫100+t dt.

I normally break it into two parts of ∫ 100 dt + ∫ t dt, getting: 100t + (t^2)/2 + c
But in one of our practice exam questions the answer used the substitution method:
u = 100+t
du = 1 dt
∫ u du = (u^2)/2 + c = ( (100+t)^2 )/2 + c

both methods are valid yet seem to get different results. I may be missing some key way to arrange one answer into the other. But I really don't understand what's happening and which method is correct.

Wait, I just realized what happened..... Sorry please delete this thread. The answers are the same, I just kept on failing with the expansion.

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Hi Ledge!

 Quote by Ledge 1. The problem statement, all variables and given/known data A very simple integration of ∫100+t dt. I normally break it into two parts of ∫ 100 dt + ∫ t dt, getting: 100t + (t^2)/2 + c But in one of our practice exam questions the answer used the substitution method: u = 100+t du = 1 dt ∫ u du = (u^2)/2 + c = ( (100+t)^2 )/2 + c both methods are valid yet seem to get different results. I may be missing some key way to arrange one answer into the other. But I really don't understand what's happening and which method is correct. Thanks for any help :)
Any integral, despite which method you use, gives you the same answer(+c). Did you try expanding out your second answer? Remember, any term without the variable in it is essentially a constant and you can let it be included in c.

 Quote by Infinitum Hi Ledge! Any integral, despite which method you use, gives you the same answer(+c). Did you try expanding out your second answer? Remember, any term without the variable in it is essentially a constant and you can let it be included in c.
Yeah thanks,
I am a bit tired studying for exams haha :P. I kept getting the expansion wrong making the answers different.

Thanks though :)

## Different methods of Integration for addition, results differ?

 Quote by Ledge Yeah thanks, I am a bit tired studying for exams haha :P. I kept getting the expansion wrong making the answers different. Thanks though :)
What did you do?

Edit : Ah, nvm.