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B Total area enclosed between ln(x) and sin^2(2x)-cos(3x)+1

  1. Jun 10, 2016 #1
    I understand the theory behind this type of question well enough; you solve ln(x)=sin^2(2x)-cos(3x)+1 to find the x values at the points of intersection, and then set up definite integrals over the domains of said x-values, subtracting whichever function is below the other for a specific domain.

    However, when doing this particular question I realised I needed to add 10 definite integrals together to obtain the total area, which seems rather excessive to me. So I was just wondering if there's a faster way of doing this question? Thank you for your help. (And in case you're wondering the answer should be 9.7435)
     
  2. jcsd
  3. Jun 11, 2016 #2

    mfb

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    Where does that problem come from? The equation doesn't even have an analytic solution, so it has to be ugly numeric integration, and I don't see the point of choosing functions that intersect so often.
     
  4. Jun 11, 2016 #3
    It was off an old work sheet from a couple of decades back that I got given as revision because I finished everything else early. I don't have the sheet anymore but I had this question written down because I found it particularly odd. The graphs intersect 11 times which is more than usual but still not too bad. I'm just curious though if there's a faster way to get the answer than setting up 10 definite integrals
     
  5. Jun 11, 2016 #4

    mfb

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    Nothing that would really help, as you have to take care of the signs in some way.
     
  6. Jun 11, 2016 #5
    Okay, thank you for the help
     
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