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Math Help - Integration - Find the area

  1. #1
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    Integration - Find the area

    1. Find the area of the finite region bounded by the curve with equation y = coth x, the x-axis and the lines x =2 and x = 4.

    2. The finite region R is bounded by the curves with equations y = cosh x, y = sinh x. the y-axis and the line x=1. Find the area of R.
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  2. #2
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    Quote Originally Posted by geton View Post
    1. Find the area of the finite region bounded by the curve with equation y = coth x, the x-axis and the lines x =2 and x = 4.

    2. The finite region R is bounded by the curves with equations y = cosh x, y = sinh x. the y-axis and the line x=1. Find the area of R.
    Where are you stuck? Setting up the integrals? Solving the integrals?

    Please show what work you've done towards getting the answers.
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    is up to his old tricks again! Jhevon's Avatar
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    Did you draw the graphs to see what is going on?

    Quote Originally Posted by geton View Post
    1. Find the area of the finite region bounded by the curve with equation y = coth x, the x-axis and the lines x =2 and x = 4.
    \int_2^4 \coth x~dx

    2. The finite region R is bounded by the curves with equations y = cosh x, y = sinh x. the y-axis and the line x=1. Find the area of R.
    \int_0^1 (\cosh x - \sinh x)~dx
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    Quote Originally Posted by mr fantastic View Post
    Where are you stuck? Setting up the integrals? Solving the integrals?

    Please show what work you've done towards getting the answers.
    For 1,

    Use the identity coth x = cosh x/sinh x = (sinh x cosh x)/(sinh^2 x)

    But sinh^2 x ≡ cosh^2 x 1
    So weve coth x = (sinh x cosh x)/ (cosh^2 x - 1) = sinh 2x /( cosh^2 x - 1)

    If I write cosh x = t, then sinh dx/dt = 1

    From this, Ive great problem.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by geton View Post
    For 1,

    Use the identity coth x = cosh x/sinh x ...
    from here, why not just make a substitution u = sinh x? why are you killing yourself?
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    Quote Originally Posted by Jhevon View Post
    Did you draw the graphs to see what is going on?
    I didn't draw the graph & it is one of my great problem.

    \int_0^1 (\cosh x - \sinh x)~dx
    Thank you for this.
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