# FP2 Integration

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#1
Using t = tan(x/2), integrate 1/1-sinx
I have differentiated t and got dt/dx = 1/2 sec^2(x/2) and then rearranged to get dx = 2dt/sec^2(x/2). So I know dx = 2dt/(1+t^2) but I'm not sure what to do with the sinx.
0
4 months ago
#2
A standard result you should know if doing the "t = tan x/2" substitution is that sin x = 2t/(1+t^2).
1
#3
(Original post by DFranklin)
A standard result you should know if doing the "t = tan x/2" substitution is that sin x = 2t/(1+t^2).
Ah really? Tbf, this is OCR and I'm doing OCR MEI but I have never come across this before. I didn't think it was that different between exam boards.
0
4 months ago
#4
(Original post by Toast210)
Ah really? Tbf, this is OCR and I'm doing OCR MEI but I have never come across this before. I didn't think it was that different between exam boards.
I don't know what's officially in any exam board, but if you are using that substitution you should work out how and remember how to express sin x, cos x and tan x in terms of t.
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#5
(Original post by DFranklin)
I don't know what's officially in any exam board, but if you are using that substitution you should work out how and remember how to express sin x, cos x and tan x in terms of t.
Thanks I appreciate it. Do you know where I could find the proofs for these expressions? I find it easier to remember them if I know how they are derived.
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4 months ago
#6
(Original post by Toast210)
Thanks I appreciate it. Do you know where I could find the proofs for these expressions? I find it easier to remember them if I know how they are derived.
https://www.examsolutions.net/tutorials/the-t-formulae/
1
4 months ago
#7
Useful for integrating trigonometric functions in rational form:

https://www.math24.net/weierstrass-substitution
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