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simple integration question

This may seem like a really obvious question but I can't seem to work out how to do this integration:

image.jpeg

I've tried substitution but it's only made the whole thing more complicated. Any ideas?
Reply 1
Try x=52sinht \displaystyle x= \frac{\sqrt 5}{2} \sinh t
(edited 8 years ago)
Reply 2
It looks like there's been an error whilst giving you this question, it's quite tedious and annoying. There's the hyperbolic trig sub as the above user has pointed out or x5tanx2x \mapsto \frac{\sqrt{5}\tan x}{2} which gets you 52sec3xdx\frac{5}{2} \int \sec^3 x \, \mathrm{d}x where a standard reduction formulae gets you where you want to go.
Original post by B_9710
Try x=52sinht \displaystyle x= \frac{\sqrt 5}{2} \sinh t


thank you! i don't think i've been taught trigonometric substitution, yet this is a question in the AQA fp2 text book so i'm guessing i have to learn it.
Reply 4
Original post by XOR_
How about differentiating y=(4x^2+5)^3/2; therefore dy/dx = (8x)(3/2)(4x^2+5)^(1/2)?


Nopes.
Original post by Zacken
Nopes.

Ah kay
is this supposed to be in the AQA FP2 specification? i have no recollection of having learnt it! :-/
Reply 7
Original post by tanyapotter
is this supposed to be in the AQA FP2 specification? i have no recollection of having learnt it! :-/


Have you learnt about hyperbolic functions?
Original post by Zacken
Have you learnt about hyperbolic functions?


yes. i know up to integrals which integrate to inverse hyperbolic functions but i'm pretty sure i don't know how to substitute trig functions in to integrate
Reply 9
Original post by tanyapotter
thank you! i don't think i've been taught trigonometric substitution, yet this is a question in the AQA fp2 text book so i'm guessing i have to learn it.


Well there is not a specific section on integration using hyperbolic functions - you have simply been made aware of the hyperbolic functions in FP2 - tools which can be used for integration.
Reply 10
Original post by tanyapotter
yes. i know up to integrals which integrate to inverse hyperbolic functions but i'm pretty sure i don't know how to substitute trig functions in to integrate


I'm fairly sure you should... it's on Edexcel FP2 that's for sure. Do you have a link to the FP2 AQA specification?
Original post by Zacken
I'm fairly sure you should... it's on Edexcel FP2 that's for sure. Do you have a link to the FP2 AQA specification?


image.jpeg

this screenshot shows everything that comes under inverse trig and hyperbolics and i've covered all of this content
Original post by Zacken
I'm fairly sure you should... it's on Edexcel FP2 that's for sure. Do you have a link to the FP2 AQA specification?


Wait wut? You sure that's not FP3 Edexcel?
Reply 13
Original post by Student403
Wait wut? You sure that's not FP3 Edexcel?


:facepalm: Yeah, that's what I meant. I mashed all my learning of C1-4 together and mashed FP2-3 together so I don't know what's in one and not the other. Thanks. :colondollar:
Original post by Zacken
:facepalm: Yeah, that's what I meant. I mashed all my learning of C1-4 together and mashed FP2-3 together so I don't know what's in one and not the other. Thanks. :colondollar:


Typical you learning so fast :3

All good :biggrin:


Original post by tanyapotter
x


:wavey:
Original post by Student403
Typical you learning so fast :3

All good :biggrin:




:wavey:

that's such a relief. i've spent so long trying to work it out! :biggrin: thanks

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