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Math Help - Integration

  1. #1
    Member WhoCares357's Avatar
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    Integration

    I have to integrate 2dx/sin(x)^2.

    The calculator gave me the answer of -2/tan(x), but I'm not sure how to get there.
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  2. #2
    Member Nacho's Avatar
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    Which the derivative of cotan(x) ?
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  3. #3
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    Yes. How do you integrate sin(x)^2 into tan(x)? Do you have to substitute something?
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  4. #4
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    note that \frac{2}{\sin^2{x}} = 2\csc^2{x}
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  5. #5
    Member WhoCares357's Avatar
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    Quote Originally Posted by skeeter View Post
    note that \frac{2}{\sin^2{x}} = 2\csc^2{x}
    But how does that turn into 2/tan(x)? wouldn't it just be 2tan(x)?
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  6. #6
    Member Nacho's Avatar
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    Quote Originally Posted by Nacho View Post
    Which the derivative of cotan(x) ?
    <br />
\left( {\cot x} \right)^\prime   =  - \csc ^2 x \Rightarrow \cot x =  - \int {\csc ^2 xdx}  \Leftrightarrow \frac{2}<br />
{{\tan x}} =  - \int {\frac{2}<br />
{{\sin ^2 x}}dx} <br />
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  7. #7
    Member WhoCares357's Avatar
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    Okay. I get it now. There are two substitutions. Once to get csc from sin and another time to get tan from cot.

    Thank you.
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