DIFFICULT integration question :S (1 Viewer)

[freezeice04]

Integration Question

How do I do this question??

 

[mirakon]

1. well on the substitution step you have x=u^2. It follows by differentiating:

dx/du=2u

Therefore dx= 2u du

So what you end up with inside the integral is

2u/(u^2 + u)

2. Note that you have to change the limits in correspondence with the new value so when x=4 u=2 and x=1 u=1. Therefore new limits are 2 and 1.

3. Integral simplifies into 1/(u+1) between the limits 2 and 1.
4. This is a fairly standard log integration from now on.
5. So integral is ln(3)-ln(2)
6. This simplifies into ln(3/2)

 

[red-butterfly]

final answer is actually
2( ln 3/2)

When dividing though by u to simplify, you forgot about the 2

 

[mirakon]

^^^thank you for the correction

 

[red-butterfly]

you're welcome

 

[hscishard]

the integrand is 2/(u+1)
[2log(u+1)] and just follow mirakons steps

Wow is my bos delayed or what?

 

[red-butterfly]

the integrand is 2/(u+1)
[2log(u+1)] and just follow mirakons steps

Wow is my bos delayed or what?

Yeah bos is heaps delayed atm... So freaking annoying and having all those dead threads around is making going around this site annoying as hell!

 

[freezeice04]

Oh yeah thanks I differentiated incorrectly lol!