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

• B
• Saracen Rue
In summary, the conversation discusses the theory of solving ln(x)=sin^2(2x)-cos(3x)+1 and setting up definite integrals over the domains of x-values. It is mentioned that there may be a faster way to solve this particular question, given that there are 11 points of intersection between the two functions. However, it is noted that there is no convenient way to simplify the process.

#### 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)

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.

mfb said:
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

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

mfb said:
Nothing that would really help, as you have to take care of the signs in some way.
Okay, thank you for the help