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Math Help - Integration

  1. #1
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    Integration

    Integral [(cosx)^3-(sinx)^2]dx/(cosx)2

    Can i cancel the cosx leaving cosx in numerator before I integrate?

    If anyone could help with integrating this problem -
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by weezie23 View Post
    Integral [(cosx)^3-(sinx)^2]dx/(cosx)2

    Can i cancel the cosx leaving cosx in numerator before I integrate?

    If anyone could help with integrating this problem -
    You have the right idea.

    Split up the integrand:

    \frac{\cos^3x-\sin^2x}{\cos^2x}=\frac{\cos^3x}{\cos^2x}-\frac{\sin^2x}{\cos^2x}=\cos x-\tan^2x

    Now can you integrate \int \cos x-\tan^2x\,dx?


    hint: \tan^2x=\sec^2x-1


    I hope this clarifies things!

    --Chris
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  3. #3
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    integrate = sinx-tanx-1

    b/c sec^2x -1 = tan^2x and Int.sec^2xdx= tanx+c



    Quote Originally Posted by Chris L T521 View Post
    You have the right idea.

    Split up the integrand:

    \frac{\cos^3x-\sin^2x}{\cos^2x}=\frac{\cos^3x}{\cos^2x}-\frac{\sin^2x}{\cos^2x}=\cos x-\tan^2x

    Now can you integrate \int \cos x-\tan^2x\,dx?


    hint: \tan^2x=\sec^2x-1


    I hope this clarifies things!

    --Chris
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by weezie23 View Post
    integrate = sinx-tanx+1

    b/c sec^2x -1 = tan^2x and Int.sec^2xdx= tanx+c
    VERY close...look at what I highlighted in red. First, it should be plus, not minus. Secondly, do you know what you forgot to do to the last term? Also, you forgot the constant of integration...

    --Chris
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  5. #5
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    or

    or i should say sinx-tanx + c
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  6. #6
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    or

    sinx-tanx -x +c
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  7. #7
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by weezie23 View Post
    or i should say sinx-tanx + c
    Not quite...

    \int \cos x-\sec^2x+1\,dx=\sin x-\tan x+\text{   }+C

    Fill in the blank...

    --Chris
    Last edited by Chris L T521; July 30th 2008 at 07:10 PM. Reason: typo
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  8. #8
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    last time

    sinx-tanx+x+c
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  9. #9
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by weezie23 View Post
    sinx-tanx -x +c
    Make it plus, and then you have it

    --Chris
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  10. #10
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by weezie23 View Post
    sinx-tanx+x+c
    Good. You have it now.

    --Chris
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