Motion and Integration question.... (1 Viewer)

[16021991]

Hi Everyone,

Just doing some past paper questions and I'm looking at 2007 paper - Question 5 - part (b) (iv) for those of you playing at home...

And Success One says that the integral of 2t/(16 + t^2) = loge(16 + t^2) + C

Can someone show me how please??

I get t^2 over 16t + t^3/3 + C myself..... but obviously I'm wrong.....

Thanks everyone !!!!

 

[gurmies]

Okay, what you have done is essentially split the fraction in a mathematically incorrect manner (I think). Recall that A/(B+C) =/= A/B + A/C. What you have there is an integral in the form f'(x)/f(x) which is always ln|f(x)| + C.

 

[fayad158]

Hi Everyone,

Just doing some past paper questions and I'm looking at 2007 paper - Question 5 - part (b) (iv) for those of you playing at home...

And Success One says that the integral of 2t/(16 + t^2) = loge(16 + t^2) + C

Can someone show me how please??

I get t^2 over 16t + t^3/3 + C myself..... but obviously I'm wrong.....

Thanks everyone !!!!

its top/differential of the bottom x ln(bottom) so 2t/2tln(16+t^2) + c which just becomes ln(16+t^2) + c

 

[untouchablecuz]

 

[16021991]

Ohhhhhhh of course why don't I have that rule written down? Thank you so much guys I truly appreciate the swift replies thanks again

 

[untouchablecuz]

the maths nerds are here to help</br>

</br>

 

[jet]

Hahahahahah +1 (I have to spread it around though).

 

[boxhunter91]

its top/differential of the bottom x ln(bottom) so 2t/2tln(16+t^2) + c which just becomes ln(16+t^2) + c

Thats the rule.