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Math Help - integration

  1. #1
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    integration

    Express in terms of and .
    Hence evaluate .

    How would you solve this question?
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  2. #2
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    Hello,
    Quote Originally Posted by Haris View Post
    Express in terms of and .
    Hence evaluate .

    How would you solve this question?
    We know that \cosh(x-y)={\color{red}\cosh(x)\cosh(y)}-\sinh(x)\sinh(y) and \cosh(x+y)={\color{red}\cosh(x)\cosh(y)}+\sinh(x)\  sinh(y)

    Add them up :

    \cosh(x-y)+\cosh(x+y)=2 \cosh(x)\cosh(y)

    Hence -\cosh(x)\cosh(y)=-\frac 12 (\cosh(x-y)+\cosh(x+y))

    Let y=2x and transform your integral.
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  3. #3
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     <br />
\int-cosh(x)cosh(2x)dx<br />
    =-\frac{1}{2} \int cosh(3x)+cosh(-x)dx

    =\frac{1}{2}sinh(-x)-\frac{1}{6}sinh(3x)+C

    Is this correct?
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  4. #4
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    Quote Originally Posted by Haris View Post
     <br />
\int-cosh(x)cosh(2x)dx<br />
    =-\frac{1}{2} \int cosh(3x)+cosh(-x)dx

    =\frac{1}{2}sinh(-x)-\frac{1}{6}sinh(3x)+C

    Is this correct?
    Yes

    But remember that sinh is an odd function and hence \sinh(-x)=-\sinh(x)
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