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# Integration by substitution Watch

1. hi there, i have just been working through a problem and have done all i can do, but i could not solve it, if anybody could offer advice it would be appreciated
The question had a first part gives x= 1/sin(θ) and asks for dx/dθ which i got to be -cosec(θ) cot(θ)

This is the tricky part:
Use the substitution x = cosec(θ) to find the integral of

1 / [x^2 · (x^2 - 1)^0.5] dx with an upper limit of 2 and lower limit of sqrt2

i have got to a point (and have left the limits for now) where i have the integral sign with this in it:

cosec(θ)cot(θ) / [cosec^2 (θ) · sqrt( cot^2 (θ)) ]

i wasn't sure if it was right to simply the inside of the integral part to:

1 / [ cosec(θ)·cot(θ) ]

i really just haven't an idea of where to go from here, sorry it looks horrible
2. (Original post by callous-b)
hi there, i have just been working through a problem and have done all i can do, but i could not solve it, if anybody could offer advice it would be appreciated
The question had a first part gives x= 1/sin(θ) and asks for dx/dθ which i got to be -cosec(θ) cot(θ)

This is the tricky part:
Use the substitution x = cosec(θ) to find the integral of

1 / [x^2 · (x^2 - 1)^0.5] dx with an upper limit of 2 and lower limit of sqrt2

i have got to a point (and have left the limits for now) where i have the integral sign with this in it:

cosec(θ)cot(θ) / [cosec^2 (θ) · sqrt( cot^2 (θ)) ]

i wasn't sure if it was right to simply the inside of the integral part to:

1 / [ cosec(θ)·cot(θ) ]

i really just haven't an idea of where to go from here, sorry it looks horrible
You've simplified the inside of your integral incorrectly. Re-check it carefully.
3. (Original post by BananaPie)
You've simplified the inside of your integral incorrectly. Re-check it carefully.
Thank you i have found it now

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