How to integrate this

[Arrow_Raider]

Alright, I am not in calculus, but for some reason I am learning some calculus stuff on my own... I am actually currently a senior at highschool and taking a precalc math class.

When trying to integrate the problem located in Figure A at the bottom, I attempted integration by parts and came up with what is located in Figure B. However, when I have Mathematica calculate the integral, it gives me what is located in Figure C. When plotting these 2 functions(Fig B and Fig C), we get what is shown in Figure D. The function located in Figure D is has a restricted domain for any x values lower than 0. My function has the same domain restrictions as the original function, sqrt(x^2+x). As you can see, for the positive values of x, my function and the actual integral function do not match exactly. The error is greater than any possible calculation preciseness errors that could be caused when graphing. So my question is, what method would one use to go about integrating this function? Was using integration by parts the right idea but implemented wrong? Or is that not a valid method for this problem and a different method must be used?

[dglienna]

I think you posted in the wrong forum. this is chit chat, where the answer to any math problem is always going to be "42"

send a PM to martinlliss and ask him to move it.

[timeshifter]

f'(x)=42

[Arrow_Raider]

haha....

well, i found out i did integration by parts wrong anyways... if integration by parts is attempted on this correctly, you get stuck and it gets you no where... so integration by parts can not be used on this problem. (what happens is, is you get this integral of a more complex function containing the original function sqrt(x^2+x) in it, which is what you were trying to get rid of, not reproduce)

[JPicasso]

It's been 8 years since I had to do an integral.

Looking at that makes my brain hurt.

makes me wonder if I really ever knew how to do integrals or if my memories are just some sort of vast alien coverup. I'm probably an al-kaidis... al-quia..

kwada?

Al Keda?

Al quidia?

cicadia?

paradeah




nevermind.

[plenderj]

Alright, I am not in calculus, but for some reason I am learning some calculus stuff on my own...

That's because you're a geek
Anyway, try differentiating your answer and see does it yield a similar answer to the original Integral?

[timeshifter]

I'm trying to find a functional formula that can determine all prime numbers...


You wanna talk geeky? I win.

[plenderj]

Sieve of Eratosthenes

[Arrow_Raider]

That's because you're a geek
Anyway, try differentiating your answer and see does it yield a similar answer to the original Integral?

Indeed...

The problem with differentiating the integral is that the integral is only defined for when x is postive. However, the original function was only restricted -1 < x < 0. Thus, when differentiating the integral, you get a really nasty function...(since of course, when differentiating the integral, the function can only be defined when x is positive)


Timeshifter -
Many people are trying/have tried to do that... they have all failed

[Arrow_Raider]

Alright, i talked to my math teacher at school, and she didn't know what to do, so then she talked to one of the calc teachers, apparently, you can't integrate this function by hand. There are no techniques to do it i guess... the only way is by using a program like i used.