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Integration (2 Viewers)

Drongoski

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Thanks gurmies...

I have a little problem again here...

The question was:



The answer in the back was:



I put it through Wolfram Mathematica and got:



I thought the answer would just be:


Which is the correct answer, and what is ArcSinh??

Thanks
Looks like yr answer sin^-1(x/3) + C is correct. When u differentiate it it gives back the integrand.
 

Drongoski

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Hyperbolic functions of x




sinh^-1( x) is just the hyperbolic analogue of circular version sin^-1 (x)
 
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cutemouse

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Yes I typed the question wrong... -_-

The correct question is:



Can anybody do it please?

Thanks =D
 

azureus88

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[maths]$Let$\ x=3\sin\phi \\dx=3\cos\phi\, d\phi[/maths]

[maths]\int \sqrt{9-x^2}dx\\=\int (3\cos\phi )(3\cos\phi )d\phi \\=9\int \cos^2\phi d\phi \\=\frac{9}{2}\int (1+\cos2\phi) d\phi \\=\frac{9}{2}(\phi +\frac{1}{2}\sin2\phi )+c\\=\frac{9}{2}\sin^{-1}\frac{x}{3}+\frac{9}{2}(\frac{x}{3})(\frac{\sqrt{9-x^2}}{3})+c\\=\frac{9}{2}\sin^{-1}\frac{x}{3}+\frac{x\sqrt{9-x^2}}{2}+c[/maths]

Alternatively, you could do it by parts if you don't lik substituting stuff back in.
 
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cutemouse

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Hi, I've yet again have one more question...



Thanks
 
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Trebla

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Assuming you've typed the question correctly, you should be able to do it yourself. Just expand it and integrate like usual...
 

cutemouse

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*doh* Thanks Trebla... I'm really off the pace today :(

Edited with the correct question
 

cutemouse

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Hi Thanks for that...

I have another one from hell :( Could someone please help me? Thanks



And yes this is the correct one, I've double checked!
 

lolokay

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again, just do it by parts

d/dx ln(x+sqrt[x^2-1]) = 1/sqrt[x^2-1]
then just a basic application of ibp
 

cutemouse

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Thanks for that... I have one more question :( As you can tell it's the weekend, and I'm working through exercises...



Thanks
 

Trebla

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Thanks for that... I have one more question :( As you can tell it's the weekend, and I'm working through exercises...



Thanks
Hint:

 
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gurmies

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Yeah dude, practise being able to transform stuff like Trebla showed you, it's really useful and logical.
 

Trebla

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Ok, i just edited a minor error as mentioned by gurmies.



The first integral does NOT give a logarithm. Apply the reverse chain rule or use the substitution u = - 2 + 3x - x².

For the second integral, complete the square of the expression inside the square root and you end up with a standard integral.
 

cutemouse

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Thanks Trebla... my bad...

Sorry guys but another question... This one's annoying as when I'm trying to fiddle around with trig integrals, I have to deal with tan(pi/2) not being defined and cot0 not being defined :(



Thanks
 

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