The Student Room Group

Intergral sub

struggling to show the (1+t^-2)/2 part, I've tried showing it directly and also tried showing it from the RHS but can't seem to factorise into anything usefulScreenshot 2022-06-25 at 16.49.11.pngIMG_8E8FF96D204C-1.jpeg
(edited 1 year ago)
Original post by Student 999
struggling to show the (1+t^-2)/2 part, I've tried showing it directly and also tried showing it from the RHS but can't seem to factorise into anything usefulScreenshot 2022-06-25 at 16.49.11.pngIMG_8E8FF96D204C-1.jpeg


I’d say let the x^2+1=t instead of the full thing, if you want me to follow that through to see if i get anywhere let me know.
Original post by RandomE
I’d say let the x^2+1=t instead of the full thing, if you want me to follow that through to see if i get anywhere let me know.


Don't think that'll work since you want the f(t) group aswell
IMG_C2AA40805461-1.jpeg

I've managed to show it now but would there have been a shorter way about it?
(edited 1 year ago)
For the second part I could directly just do my substitution from part a and get the answer, what I did is referenced part a to save time but my explanation on how they're linked feels mathematically weak?IMG_A470F2C20473-1.jpeg
(edited 1 year ago)
Don’t reckon so
Original post by Student 999
For the second part I could directly just do my substitution from part a and get the answer, what I did is referenced part a to save time but my explanation on how they're linked feels mathematically weak?IMG_A470F2C20473-1.jpeg

Id guess that would be the solution they're expecting. Not sure why you think its weak.
Original post by mqb2766
Id guess that would be the solution they're expecting. Not sure why you think its weak.


I meant as in the why I can directly use f(t)= t^-3, would I not need to give some form of explanation?
(edited 1 year ago)
Original post by Student 999
I meant as in the why I can directly use f(t)= t^-3, would I not need to give some form of explanation?


Thats the form of the function in the original integral, so youre simply applying the general result from part a) to a particular function.
(edited 1 year ago)

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