kabilan13
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how do I do this?

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kabilan13
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integrate (1/(sect-1))
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username456717
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(Original post by kabilan13)
integrate (1/(sect-1))
What have you done so far?
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kabilan13
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(Original post by nebelbon)
What have you done so far?
i tried to substitute u=sect but it didnt work.
i also tried to multiply top and bottom by cos(t) but couldnt intergrate.
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TeeEm
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(Original post by kabilan13)
how do I do this?

use the substitution u = tan(x/2)


then secu = (1+u2)/(1-u2)
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username456717
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(Original post by kabilan13)
i tried to substitute u=sect but it didnt work.
i also tried to multiply top and bottom by cos(t) but couldnt intergrate.
What other substitutions could you try?

What other methods are there to be used in integration?

Can you split the fraction up?
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TeeEm
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(Original post by nebelbon)
What other substitutions could you try?

What other methods are there to be used in integration?

Can you split the fraction up?

(Original post by kabilan13)
i tried to substitute u=sect but it didnt work.
i also tried to multiply top and bottom by cos(t) but couldnt intergrate.
look at post 15
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username456717
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(Original post by TeeEm)
look at post 15
I know how to do it, but you are not supposed to give the answer straight away.
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Mr M
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I'm sorely tempted to create a sticky about the spelling of 'integration'.
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davros
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(Original post by nebelbon)
I know how to do it, but you are not supposed to give the answer straight away.
He hasn't exactly given the answer away - he's just pointed out what an appropriate substitution would be.

Tbh I'd expect the OP's textbook to give guidance on what substitution is appropriate when integrating a rational function of sin and cos, but the OP has probably forgotten this
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tiny hobbit
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(Original post by Mr M)
I'm sorely tempted to create a sticky about the spelling of 'integration'.
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newblood
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For the first integral why dont you rewrite it in terms of cos and then see what multiplying top and bottom by cosx will give you.
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TeeEm
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(Original post by newblood)
For the first integral why dont you rewrite it in terms of cos and then see what multiplying top and bottom by cosx will give you.
Your suggestion will work, so so will the substitution t = tan(tx/2) which I suggested for the second integral.

However the best method to integrate secx is to write it as secx/1, multiply top and bottom by [secx + tan], expand and simplify and then notice that numerator is the exact derivative of denominator.

I think our friend asks for the second integral only
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TeeEm
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(Original post by kabilan13)
integrate (1/(sect-1))
method A, Standard way, using little t identities

use the substitution u=tan(t/2)
then sect = (1+u2)/(1-u2)


Method B
multiply top and bottom by (sect+1)
bottom gives a very well known trig identity
you split the fraction and tidy up ... bit messy
eventually after a bit of work you get cot t cosect + cot2t
the first "lump" is an exact differential the second can be switched into cosec2t - 1, which also integrates.
There is a problem with this method if your limits cross the discontinuity, i.e. sect + 1 which we multiplied top and bottom must not be zero.


METHOD C
multiply top and bottom by cost first

write the cost in the top, as cos2(t/2) - sin2(t/2)
write the cost in the bottom as 2cos2(t/2) - 1
Split fraction to 1/2 -1/2tan2(t/2)
etc etc...
Again potential problem in definite integration as in method B.


I wish I could point you to download my "mother of all resources" when it comes to integration but I do not want to get done for advertising.
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username456717
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(Original post by davros)
He hasn't exactly given the answer away - he's just pointed out what an appropriate substitution would be.

Tbh I'd expect the OP's textbook to give guidance on what substitution is appropriate when integrating a rational function of sin and cos, but the OP has probably forgotten this
I'd expect it to be given too - it is rare when they aren't.
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