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Math Help - integrating inverse trigonometry

  1. #1
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    integrating inverse trigonometry

    could someone please help me with the integration of cos-1x and tan-1x?
    i know that we have to draw the cos and tan graphs and somehow calculate the areas through the method of integration by parts
    thankyouuuu !
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  2. #2
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    Quote Originally Posted by christina View Post
    could someone please help me with the integration of cos-1x and tan-1x?
    i know that we have to draw the cos and tan graphs and somehow calculate the areas through the method of integration by parts
    thankyouuuu !

    For example: u=\arccos x\Longrightarrow\,u'=-\frac{1}{\sqrt{1-x^2}}\,,\,\,v'=1\Longrightarrow\,v=x , so integrating by parts:

    \int\arccos x\,dx=x\arccos x+\int\frac{x}{\sqrt{1-x^2}}\,dx=x\arccos x-\frac{1}{2}\int\frac{-2x}{\sqrt{1-x^2}}\,dx= x\arccos x-\sqrt{1-x^2}+C

    Now you do the other one following the lines above.

    Tonio
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