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Substitution for Definite Integrals with Trig
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username970964
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#1
Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
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WishingChaff
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#2
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#2
The first line is incorrect anyway.
Given
, what is 
?
Given
, what is ?
(Original post by Airess3)
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Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
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username970964
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#3
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Anonymous_0749
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(Original post by Airess3)
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Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
[arctan(x) ] pi/4 and 0 limits ; you get the formula in the formula book ? well for mei we do (FP2)
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WishingChaff
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#5
Yes, pretty much. You get that:
Now, you need to substitute this into your integral, along with the correct limits. But, before doing this, do you know a trigonometric identity that might help here?
Once this is done, what does your integral now simplify too? It should, of course, be an integral of the dummy variable
Now, you need to substitute this into your integral, along with the correct limits. But, before doing this, do you know a trigonometric identity that might help here?
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Once this is done, what does your integral now simplify too? It should, of course, be an integral of the dummy variable
(Original post by Airess3)
sec^2 θ
sec^2 θ
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TeeEm
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(Original post by Airess3)
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Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
Are steps missing between lines 1 and 2? have no idea how the equation changed so drastically.
PDF.pdf
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username970964
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#7
But can you explain how you got from the step before to 1/2 + 1/2 cos2θ dθ in the third line in example 3? Is it derived from a certain trig identity?
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TeeEm
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(Original post by Airess3)
Thanks!
But can you explain how you got from the step before to 1/2 + 1/2 cos2θ dθ in the third line in example 3? Is it derived from a certain trig identity?
Thanks!
But can you explain how you got from the step before to 1/2 + 1/2 cos2θ dθ in the third line in example 3? Is it derived from a certain trig identity?
cos2x = 1/2 +1/2cos(2x)
sin2x = 1/2 -1/2cos(2x)
they are rearrangements of cos(2x) trigonometric identities
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username970964
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#9
(Original post by TeeEm)
standard identities useful in integration
cos2x = 1/2 +1/2cos(2x)
sin2x = 1/2 -1/2cos(2x)
they are rearrangements of cos(2x) trigonometric identities
standard identities useful in integration
cos2x = 1/2 +1/2cos(2x)
sin2x = 1/2 -1/2cos(2x)
they are rearrangements of cos(2x) trigonometric identities
So I got the answer to be 1? Is that the right answer or did something go wrong?
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TeeEm
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#10
(Original post by Airess3)
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So I got the answer to be 1? Is that the right answer or did something go wrong?
So I got the answer to be 1? Is that the right answer or did something go wrong?
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username970964
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#11
(Original post by TeeEm)
I should be able to read it but at the moment I have forgotten how to reflect my head
I should be able to read it but at the moment I have forgotten how to reflect my head
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TeeEm
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#12
(Original post by Airess3)
Ok, here's the pictures, yesterday my phone ran out of charge so I had to use the camera from my laptop.
Ok, here's the pictures, yesterday my phone ran out of charge so I had to use the camera from my laptop.
∫ 1 dθ integrates to θ, with limits in θ
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#13
(Original post by TeeEm)
the first 4 lines are correct then it is wrong
∫ 1 dθ integrates to θ, with limits in θ
the first 4 lines are correct then it is wrong
∫ 1 dθ integrates to θ, with limits in θ
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