Integration Question (1 Viewer)

[Will Hunting]

Use the substitution t = u^2 - 2 to find the following indefinite integral:

S [1/sqrt(t + 2)]dt

From the relationship above,

dt/du = 2u
dt = 2udu, which is substituted for dt

Also, u^2 = t + 2,

1/sqrt(t + 2) = 1/sqrt(u^2) = 1/u

Now, integral can be written,

S [1/u x 2udu] = S 2du = 2u = 2sqrt(t + 2) (Since u = sqrt(t + 2))

Is this all cool? I'm worried that it seemed I was integrating a statement in u with respect to "t", but I'm pretty sure the equalities I used make it valid.

 

[FD3S-R]

works 100%

 

[ngai]

I'm worried that it seemed I was integrating a statement in u with respect to "t", but I'm pretty sure the equalities I used make it valid.

its fine

the question was an integration w.r.t "t"
then you transformed it into integral w.r.t "u", by let u = whatever
then you integrated the new integral (which is in u) w.r.t "u", to get an answer about u, which is then transformed back into one about t

btw "= 2sqrt(t + 2)^1/2"...dont think you need the power 1/2 if u wrote sqrt

 

[Will Hunting]

That's right - I went an index too far
Thanks for that FD3S-R and ngai. I had my Ext 1 half-yearly today and that was the only question that spun me out and broke my rhythm (not sure as to why, though). You've lifted a huge weight for me (Although perspective's something I'm still deficient in - bah, I'm allowed to blow things outta prop'n for a little while after exams! He he). Cheers.

 

[BlackJack]

Be careful in the last bit for future reference, you should write that you checked both square roots, since you used the relation u²=t+2 and not u=sqrt(t+2). The positive one is the only correct one that yields the derivative.

 

[Will Hunting]

+ C !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! It was indefinite!!!

 

[Slidey]

Let's see... you lost a mark because you forgot C?

 

[Will Hunting]

Half a mark, but, still, the wound's festering no less :'( lol

 

[Slidey]

I lost a mark for saying |2+2i|=2. *shudders*

 

[thunderdax]

I lost a mark for saying |2+2i|=2. *shudders*

Yeah, in my first 4U exam i got 48/50
lost one mark for saying 4*-4i=-8i
lost one mark for putting a dot on 3 instead of 4 on polar grid paper
I'm still hitting myself for not getting 100% on that test.

 

[haboozin]

I lost a mark for saying |2+2i|=2. *shudders*

yea exact same thing happened to me

but it was
|1 + i| and i said 1 instead of sqrt2

so i got 98 in my first term test...