- #1
wilcofan3
- 27
- 0
How do I go about finishing/calculating this?
Use a power series to approximate [tex]\int\cos 4x\log x dx[/tex] to six decimal places. (bounds are from pi to 2pi)
So I broke down the equation first:
[tex]\int\cos 4x\log x dx = \frac{1}{4}\sin 4x\log x - \frac{1}{4}\int \frac{\sin 4x}{x}dx[/tex]
Now I am using the fact that [tex]\sin x = \sum_{n=0}^\infty(-1)^n\frac{(4x)^{2n+1}}{(2n+1)!}\Rightarrow \frac{\sin x}{x} = \sum_{n=0}^\infty(-1)^n\frac{4^{2n+1}x^{2n}}{(2n+1)!}[/tex].
This is a really stupid question probably, but I don't understand how to go about finishing the problem even though I think I have the right idea.
What I don't understand is how the bounds play a part in this. Am I just calculating that last series to six decimal places?
Homework Statement
Use a power series to approximate [tex]\int\cos 4x\log x dx[/tex] to six decimal places. (bounds are from pi to 2pi)
Homework Equations
The Attempt at a Solution
So I broke down the equation first:
[tex]\int\cos 4x\log x dx = \frac{1}{4}\sin 4x\log x - \frac{1}{4}\int \frac{\sin 4x}{x}dx[/tex]
Now I am using the fact that [tex]\sin x = \sum_{n=0}^\infty(-1)^n\frac{(4x)^{2n+1}}{(2n+1)!}\Rightarrow \frac{\sin x}{x} = \sum_{n=0}^\infty(-1)^n\frac{4^{2n+1}x^{2n}}{(2n+1)!}[/tex].
This is a really stupid question probably, but I don't understand how to go about finishing the problem even though I think I have the right idea.
What I don't understand is how the bounds play a part in this. Am I just calculating that last series to six decimal places?