Antidifferentiating To \int^{2c}_{c} e^f(x)dx = 7

[snipez90]

If \int^{2c}_{c} e^f(x)dx = 7, then what is \int^{2}_{1} e^f(cx)dx?

Ok I understood that u-sub is the easiest way to solve this, but what is wrong with trying to find an antiderivative of the first expression and the second, using the FTC and substituting to get the answer? I did it that way and the teacher said I was making the assumption that C = 1 (i think 0 or 1) but he didn't explain to me why it was wrong.

 

[snipez90]

Is it wrong to say that the antiderivative of e^f(x) is e^f(x)/f'(x) + C and then applying FTC? Or does that only work for one case? I don't know if such manipulations are permissible. Just wondering if my "brute-forcing" is even correct.

 

[d_leet]

You don't know what f is, so how do you expect to find an antiderivative? And no e^f(x)/f'(x)+C is not correct, to see why what happens when you differentiate it? I think a substitution is definitely the easiest way, and off the top of my head I can't think of a different way to do it.

 

[snipez90]

totally see it now, man i was blind. thank you.