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- Homework Statement
- Find the arc length from 0-3pi for v(x)=(e^x cos(2x), e^x sin(2x), e^x)

- Relevant Equations
- Arc length formula for vector equations

The vector equation is ## v(x)=(e^x cos(2x), e^x sin(2x), e^x) ##

I know the arc-length formula is ## S=\int_a^b \|v(x)\| \,dx ##

I found the derivative from a previous question dealing with this same function, but the when I plug it into the arc-length function I get an integral that I've tried and tried but just can't get anywhere with. The complexity of the problem also makes me think that I might be approaching it from the wrong direction. Here is the integral as I understand it: $$ \int{\sqrt{ (e^{2x}) ( (-2\sin(2x) + \cos(2x))^2 + (2\cos(2x)+\sin(2x))^2 + 1 ) }} \, dx $$

I would appreciate any tips on the integral or the problem as a whole, if there's another way to solve it that I haven't seen.

I know the arc-length formula is ## S=\int_a^b \|v(x)\| \,dx ##

I found the derivative from a previous question dealing with this same function, but the when I plug it into the arc-length function I get an integral that I've tried and tried but just can't get anywhere with. The complexity of the problem also makes me think that I might be approaching it from the wrong direction. Here is the integral as I understand it: $$ \int{\sqrt{ (e^{2x}) ( (-2\sin(2x) + \cos(2x))^2 + (2\cos(2x)+\sin(2x))^2 + 1 ) }} \, dx $$

I would appreciate any tips on the integral or the problem as a whole, if there's another way to solve it that I haven't seen.