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Math Help - find the primitive of cosec^2(x)

  1. #1
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    find the primitive of cosec^2(x)

    Hey, can someone help me find the primitive of:

     cosec^2x
    the answer is  -cotx + c

    EDIT:  \int cosec^2 x
     \int sec^2(90-x)
     = tan(90-x)+ c
     = cotx + c

    But how did they get - cotx

    Thanks in advance
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by differentiate View Post
    Hey, can someone help me find the primitive of:

     cosec^2x
    the answer is  -cotx + c

    EDIT:  \int cosec^2 x
     \int sec^2(90-x)
     = tan(90-x)+ c
     = cotx + c

    But how did they get - cotx

    Thanks in advance
    \frac{d}{dx}[\cot{x}+C]=-\csc^2{x}\Rightarrow\int\csc^2{x}dx=-\cot{x}+C

    Does this make sense?
    Last edited by VonNemo19; September 25th 2009 at 07:49 PM.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    I agree completely with VonNemo however if you want to know why your method didn't work

    = -tan(pi/2 - x)

    Since you would let u = pi/2 - x (use radians always in Calculus)

    du = -dx

    result follows
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Hey Calculus26, why don't you ever use latex?
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  5. #5
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    Thanks guys
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