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

[Saracen Rue]

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 realized 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)

 

[mfb]

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.

 

[Saracen Rue]

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

 

[mfb]

Nothing that would really help, as you have to take care of the signs in some way.

 

[Saracen Rue]

Nothing that would really help, as you have to take care of the signs in some way.

Okay, thank you for the help