YAMT: What am I doing wrong?!

[agnitrate]

Ahh! This problem is driving me crazy. I'm like 100% sure it's right, but my calculator doesn't seem to agree.

y' = (t+1) / ( t * (t + 4) ) , Find y

y = integral ( (t+1) / t ) * integral ( 1 / (t+4) ) , right?

integral ( (t+1) / t ) = ln(t) + t
integral( 1 / (t+4) ) = ln( t+4 )

so...

y = ( ln(t) + t ) * ( ln ( t+4 ) ) correct?

Did I make an incorrect assumption somewhere? This is basic stuff but it's driving me crazy!

EDIT :

Ok, I figured out where I went wrong. integral of (x^3) != integral (x^2) * integral (x)
I confused it with integral of (x+x^2) = integral (x) + integral (x^2)

I still don't know how to do the problem though 🙁

-silver

 

[FrustratedUser]

Originally posted by: agnitrate
Ahh! This problem is driving me crazy. I'm like 100% sure it's right, but my calculator doesn't seem to agree.

y' = (t+1) / ( t * (t + 4) ) , Find y

y = integral ( (t+1) / t ) * integral ( 1 / (t+4) ) , right?

integral ( (t+1) / t ) = ln(t) + t
integral( 1 / (t+4) ) = ln( t+4 )

so...

y = ( ln(t) + t ) * ( ln ( t+4 ) ) correct?

Did I make an incorrect assumption somewhere? This is basic stuff but it's driving me crazy!

-silver

You forgot the constant at the end.
Derive a number, for example 2 and you get ' ' (nothing). Now integrate and you have to add the unknown constant 'C'.
Didn't check the other part.

 

[agnitrate]

I know about the constant, that's just assumed 😉

I do have an initial condition but I just wanted to find the answer first.

-silver

 

[rgwalt]

You can separate your integral into:

y = integral(1/(t+4)) + integral(1/t*(t+4))

First integral is ln(t+4)

Second integral... try finding it in integration tables or try integration by parts.

 

[eLiu]

you solve this by using partial fractions. Do a search on google or www.mathworld.com. It'll explain what they are & how to use them (i'm too lazy to type it here). Partial fractions will break that into 2 much simpler integrals that you should be able to do easily.

 

[agnitrate]

Originally posted by: eLiu
you solve this by using partial fractions. Do a search on google or www.mathworld.com. It'll explain what they are & how to use them (i'm too lazy to type it here). Partial fractions will break that into 2 much simpler integrals that you should be able to do easily.

I've been trying but I haven't been able to solve it. I'll keep trying though and post if I can't work it out.

-silver

 

[agnitrate]

Oh...my...god. I am a huge idiot.

I did it correctly with partial fractions like 10 mins ago and didn't think I did it correctly because I looked at the problem wrong!! AHHHHHHH!!!!

Thanks guys 🙂

FYI the answer of the partial fractions is :

(1/4) / t + (3/4) / (t +4)

So the answer is :

1/4 ln t + 3/4 ln (t + 4)

I am a little rusty if you can't tell 🙂

-silver

 

[rufruf44]

Originally posted by: agnitrate
Oh...my...god. I am a huge idiot.

I did it correctly with partial fractions like 10 mins ago and didn't think I did it correctly because I looked at the problem wrong!! AHHHHHHH!!!!

Thanks guys 🙂

FYI the answer of the partial fractions is :

(1/4) / t + (3/4) / (t +4)

So the answer is :

1/4 ln t + 3/4 ln (t + 4)

I am a little rusty if you can't tell 🙂

-silver

Man, I wished I'm just a little rusty. I used to eat up those problems, but now I can't even remember the formula,etc. You just tend to forgot things that you didnt use 🙁