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Integration by Substituion help!!!

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
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 1−x21-x^2 is for this substitution? Then taken the square root? :smile:
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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(edited 8 years ago)
Original post by rayquaza17
Okay so have you tried to work out what 1−x21-x^2 is for this substitution? Then taken the square root? :smile:



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

Posted from TSR Mobile


sorry meaning u as theta
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
(edited 8 years ago)
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?
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?

Posted from TSR Mobile
(edited 8 years ago)
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
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). :s-smilie:
Original post by rayquaza17
Okay I have no idea then...
As mentioned above, the typical substitution for this question would be x=sin(theta). :s-smilie:


Thanks for trying to help

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