## Proving a property of an integral

I have already solved it, but I need confirmation:

Are there other ways of proving this?

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age

Recognitions:
Homework Help
 Quote by Mike s I have already solved it, but I need confirmation: Are there other ways of proving this? Thanks in advance!
Your proof is fine (and it's the way I would've done it), except that you should explicitly define your $F(a)$. You implicitly defined it as an indefinite integral, which means $F(0) = c$, but I would prefer to define $F(a) = \int_0^a f(x) dx$, and include one more intermediary step clarifying that $\int_a^{2a} f(t) dt = \int_0^{2a} f(t) dt - \int_0^a f(t) dt = F(2a) - F(a)$. This way, I don't have to bother with the $F(0)$ term at all.

 Quote by Curious3141 Your proof is fine (and it's the way I would've done it), except that you should explicitly define your $F(a)$. You implicitly defined it as an indefinite integral, which means $F(0) = c$, but I would prefer to define $F(a) = \int_0^a f(x) dx$, and include one more intermediary step clarifying that $\int_a^{2a} f(t) dt = \int_0^{2a} f(t) dt - \int_0^a f(t) dt = F(2a) - F(a)$. This way, I don't have to bother with the $F(0)$ term at all.
Thanks a lot!