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# Tricky integration problem watch

1. Heres my working out, and was hoping someone could check it out ?
http://imgur.com/EHpu4yC

The question is dx / [ROOT (1-x^2)]

I can't use partial fractions as the questions wants me to use substitution
2. I'll give you a hint: When you see a 1+/-x^2 on the denominator, it's usually a trigonometric/hyperbolic trig substitution you need to make. Knowing that, can you think of something such that 1 - (something)^2 = (something else)^2? If you can, the root will drop out and you should see the whole integral simplify
3. (Original post by T-GiuR)
Heres my working out, and was hoping someone could check it out ?
http://imgur.com/EHpu4yC

The question is dx / [ROOT (1-x^2)]

I can't use partial fractions as the questions wants me to use substitution
You cannot use partial fractions here even if you wanted to.

after your substitution you must get

∫cosθ/√(1-sin2θ) dθ
4. (Original post by T-GiuR)
Heres my working out, and was hoping someone could check it out ?
http://imgur.com/EHpu4yC
In the 2nd line you have (incorrectly) got rid of the square root, incorrectly divided by the derivative of the substitution term when you should have multiplied, and done the division wrong (*).

It's kind of impressive, in a perverse kind of fashion...

(*) Well, I think that's what you've done - when so much goes wrong in so little space it's kind of hard to be sure.
5. (Original post by TeeEm)
You cannot use partial fractions here even if you wanted to.

after your substitution you must get

∫cosθ/√(1-sin2θ) dθ
I tried it again, and got this ?
http://imgur.com/cy9Wv6a
6. (Original post by DFranklin)
In the 2nd line you have (incorrectly) got rid of the square root, incorrectly divided by the derivative of the substitution term when you should have multiplied, and done the division wrong (*).

It's kind of impressive, in a perverse kind of fashion...

(*) Well, I think that's what you've done - when so much goes wrong in so little space it's kind of hard to be sure.
Tried it again and got this ?
http://imgur.com/cy9Wv6a
7. (Original post by T-GiuR)
Tried it again and got this ?
http://imgur.com/cy9Wv6a
Yes that's fine.
8. (Original post by T-GiuR)
I tried it again, and got this ?
http://imgur.com/cy9Wv6a

PS:
Please do not take it the wrong way.
The answer is correct but the way your work is presented is not very clear and you are running the risk if your answer is incorrect not to get any credit (even if the mistake is minute)
9. (Original post by TeeEm)

PS:
Please do not take it the wrong way.
The answer is correct but the way your work is presented is not very clear and you are running the risk if your answer is incorrect not to get any credit (even if the mistake is minute)
Thank you, and I completely understand.
I didn't have any A4 paper next to me so I had to do it in a small diary
10. (Original post by T-GiuR)
Thank you, and I completely understand.
I didn't have any A4 paper next to me so I had to do it in a small diary
no worries

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