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Babyslapmafro

  • 3 years ago

How do you find the anti-derivative of y=|x|

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  1. AravindG
    • 3 years ago
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    y=mod x has no derivative

  2. AravindG
    • 3 years ago
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    then why ask for anti derivative?

  3. Babyslapmafro
    • 3 years ago
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    I'm trying to find the area between the following two curves. \[y=\frac{ 2 }{ 1+x^2 }, y=|x|\]

  4. Babyslapmafro
    • 3 years ago
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    Between the points, x=-1,1

  5. hba
    • 3 years ago
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    Integrate.

  6. Babyslapmafro
    • 3 years ago
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    Right but how do I integrate with an absolute value of x?

  7. chethana_bhaskara
    • 3 years ago
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    integral(-1 to 0) (-x)dx+ integral(0 to 1)xdx

  8. Babyslapmafro
    • 3 years ago
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    \[\int\limits_{-1}^{1}(\frac{ 2 }{ 1+x^2 }-|x|)dx\]

  9. Babyslapmafro
    • 3 years ago
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    oh i see, i have to find two definite integrals

  10. chethana_bhaskara
    • 3 years ago
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    u get the value of that integral of |x| as 1

  11. chethana_bhaskara
    • 3 years ago
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    yea because, |x| can either be +x or -x ...so u integrate -x from -1 to 0 and +x from 0 to 1

  12. Babyslapmafro
    • 3 years ago
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    Then you just add the two areas together?

  13. chethana_bhaskara
    • 3 years ago
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    Yeah

  14. Babyslapmafro
    • 3 years ago
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    Ok could you just explain again why we use -x when find the definite integral between -1 and 0?

  15. Babyslapmafro
    • 3 years ago
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    I got the answer right, I just want to be clear as to why that is done.

  16. chethana_bhaskara
    • 3 years ago
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    because x is negative and you so u consider the negative values of x .....I actually don't have complete knowledge on this topic :/

  17. Babyslapmafro
    • 3 years ago
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    Ok well I'll ask when I get to class thanks for the help

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