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# FP2/3 Integration maths help! watch

1. Integral of sqrt of (1+t^2), using the substitution t=sinhx ?
2. (Original post by RockConcert)
Integral of sqrt of (1+t^2), using the substitution t=sinhx ?
just think of it as a normal C4 t=sinx sub except be careful with the identities (you know how the hyperbolic identities differ slightly from the trig ones)
3. (Original post by DylanJ42)
just think of it as a normal C4 t=sinx sub except be careful with the identities (you know how the hyperbolic identities differ slightly from the trig ones)
I keep trying with that approach but my answer is far too simple.. ( arsinht instead of 1/2(t(sqrt of (1+t^2))+arsinht) )
4. (Original post by RockConcert)
I keep trying with that approach but my answer is far too simple.. ( arsinht instead of 1/2(t(sqrt of (1+t^2))+arsinht) )
maybe im wrong, let me try it, 2 secs
5. integral becomes 1 + sinh^2(x)/cosh(x)

change 1 + sinh^2(x)
6. (Original post by RockConcert)
I keep trying with that approach but my answer is far too simple.. ( arsinht instead of 1/2(t(sqrt of (1+t^2))+arsinht) )
Show us your working. We can't help until you do.

Oh, and moved to maths.
7. (Original post by RockConcert)
I keep trying with that approach but my answer is far too simple.. ( arsinht instead of 1/2(t(sqrt of (1+t^2))+arsinht) )
okay got it, can you post some workings?
8. (Original post by RockConcert)
I keep trying with that approach but my answer is far too simple.. ( arsinht instead of 1/2(t(sqrt of (1+t^2))+arsinht) )
You put the differential in 'upside down'
9. (Original post by RockConcert)
Attachment 511355
As above, it should be .
10. Dt=cosh(X)dx is what you needed

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11. (Original post by RockConcert)
You got confused with your substitution. We want :

You should have recognised your mistake right away as .
12. (Original post by Louisb19)
Surely you mean ?
13. (Original post by Zacken)
Surely you mean ?
i think he means after the integration has been done, using that identity to get the answer into the correct form
14. .
15. (Original post by DylanJ42)
i think he means after the integration has been done, using that identity to get the answer into the correct form
Ah, okay.
16. (Original post by DylanJ42)
i think he means after the integration has been done, using that identity to get the answer into the correct form
true dat PRSOM
17. (Original post by Louisb19)
You got confused with your substitution. We want :

You should have recognised your mistake right away as .
Ah thank you so much, that identity (sin2x) was the key! Man I'm not going to forget that identity again..
18. (Original post by RockConcert)
Ah thank you so much, that identity (sin2x) was the key! Man I'm not going to forget that identity again..
remember it with the h on the end too. cosh
19. (Original post by EricPiphany)
remember it with the h on the end too. cosh

Don't worry that was a typo, I did use sinh2x = 2sinhxcoshx in my solution. But thank you for your concern!
20. (Original post by RockConcert)
Don't worry that was a typo, I did use sinh2x = 2sinhxcoshx in my solution. But thank you for your concern!
You're welcome xxx

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