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

  • #1
144
7
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)
 

Answers and Replies

  • #2
35,264
11,519
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.
 
  • #3
144
7
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.
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
 
  • #4
35,264
11,519
Nothing that would really help, as you have to take care of the signs in some way.
 
  • #5
144
7
Nothing that would really help, as you have to take care of the signs in some way.
Okay, thank you for the help
 

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