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# P5 trig substitution integration watch

1. got an integration

I [1/sqrt(25-4x^2) dx

there are two substitutions that you can use i think

using x=(5/2)cos u we get : -0.5arccos (2x/5)

and using x=(5/2)sin u we i get 0.5arcsin(2x/5)
are they both valid and the same, and if we get a ques likek that in an exam, which form do we use?

pk
2. (Original post by Phil23)
got an integration

I [1/sqrt(25-4x^2) dx

there are two substitutions that you can use i think

using x=(5/2)cos u we get : -0.5arccos (2x/5)

and using x=(5/2)sin u we i get 0.5arcsin(2x/5)
are they both valid and the same, and if we get a ques likek that in an exam, which form do we use?

pk
I think both are ok... but I think we'd better use the formula in the formula book.
3. (Original post by BCHL85)
I think both are ok... but I think we'd better use the formula in the formula book.
phew. cheers - realyl clears things up - been going through my solution looking for mistakes and couln't find it - the cos version is what my teacher taught us in school - sin one is the one they have in the formula book so was obviousl abit lost

thing is when you put values in - you get different result??. any explanation for this?

pk
4. (Original post by Phil23)
phew. cheers - realyl clears things up - been going through my solution looking for mistakes and couln't find it - the cos version is what my teacher taught us in school - sin one is the one they have in the formula book so was obviousl abit lost

thing is when you put values in - you get different result??. any explanation for this?

pk
If you put the limits in and get different result ... one of them is wrong
Cuz ... in general integration ... you must plus constant C with your answer , which makes it look different
5. (Original post by Phil23)
phew. cheers - realyl clears things up - been going through my solution looking for mistakes and couln't find it - the cos version is what my teacher taught us in school - sin one is the one they have in the formula book so was obviousl abit lost

thing is when you put values in - you get different result??. any explanation for this?

pk
yeah i did this whole big question from one of the solomon papers..n used a sub for x=sinh u
it all worked out..except that the answer was different to that required..
in the answer scheme it said u were to use a simpler sub by jus 'u'
puzzles me immensly
how r we meant to kno which one to use
6. (Original post by hajira)
yeah i did this whole big question from one of the solomon papers..n used a sub for x=sinh u
it all worked out..except that the answer was different to that required..
in the answer scheme it said u were to use a simpler sub by jus 'u'
puzzles me immensly
how r we meant to
exactly, and the markschemes dont have other variants either! Happened to me a few times - got diff form - peeves me off a bit!

pk
7. (Original post by Phil23)
how r we meant to
exactly, and the markschemes dont have other variants either! Happened to me a few times - got diff form - peeves me off a bit!

pk
we'll just need to hope that our ones r what they require i guess
actually..
in solomons, i havent come across a single one where u r meant to use a sub for a trig or hyperbolic
maybe its just them

at the end i guess..dont worry
hope for the best n we'll all b fine!

tho..im SO unsure its unreal
8. arcsin(t) + arccos(t) = pi/2

is the reason the answers are the same barring a constant

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