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# Integration by Substituion help!!! watch

1. I'm really stuck on this question, cant even get past the first stage, can someone help me out fully as im going nowhere

Using the substituion x=2sin(Theta) find integral of: 1/(1-x^2)^1/2
2. (Original post by questioningfox)
I'm really stuck on this question, cant even get past the first stage, can someone help me out fully as im going nowhere

Using the substituion x=2sin(Theta) find integral of: 1/(1-x^2)^1/2
Okay so have you tried to work out what is for this substitution? Then taken the square root?
3. Let 1-x^2 = U so you integrate (1/U^1/2).dx and get dx in terms of dU so you can integrate

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4. (Original post by rayquaza17)
Okay so have you tried to work out what is for this substitution? Then taken the square root?

root of 1-4sin^2(theta)??? no idea I was taught to do try to find dx/d(theta) and then sub U into the x part. Really stuck do you think you could show entire steps?
5. (Original post by questioningfox)
I'm really stuck on this question, cant even get past the first stage, can someone help me out fully as im going nowhere

Using the substituion x=2sin(Theta) find integral of: 1/(1-x^2)^1/2
are you sure it's 2sin(theta) and not just sin(theta)?
6. (Original post by questioningfox)
root of 1-4sin^2(theta)??? no idea I was taught to do try to find dx/d(theta) and then sub U into the x part. Really stuck do you think you could show entire steps?
What's your U? And dx/d(theta) simply be 2cos(theta) since sin differentiates to cos

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7. (Original post by eternaforest)
What's your U? And dx/d(theta) simply be 2cos(theta) since sin differentiates to cos

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sorry meaning u as theta
8. (Original post by aymanzayedmannan)
are you sure it's 2sin(theta) and not just sin(theta)?
yup (as in it is 2sin(theta) just checked the question again
9. (Original post by questioningfox)
root of 1-4sin^2(theta)??? no idea I was taught to do try to find dx/d(theta) and then sub U into the x part. Really stuck do you think you could show entire steps?
Yea that's right what you have there.
But I'm not convinced by this question because you should get something you can use an identity for to simplify, and I can't think of anything that would make this easier.

Is this from a textbook?
10. (Original post by questioningfox)
sorry meaning u as theta
To integrate 1/(1-4sin^2(theta))^1/2 doesn't it make more sense to let 1-4sin^2(theta) = x since then you'd be integrating 1/x^1/2?

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11. (Original post by rayquaza17)
Yea that's right what you have there.
But I'm not convinced by this question because you should get something you can use an identity for to simplify, and I can't think of anything that would make this easier.

Is this from a textbook?
Nah one of the dammed worksheets where they dont give the answers so have no idea where you are going
12. (Original post by questioningfox)
Nah one of the dammed worksheets where they dont give the answers so have no idea where you are going
Okay I have no idea then...
As mentioned above, the typical substitution for this question would be x=sin(theta).
13. (Original post by rayquaza17)
Okay I have no idea then...
As mentioned above, the typical substitution for this question would be x=sin(theta).
Thanks for trying to help

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