The problem involves evaluating the definite integral of the absolute value of a function, specifically $$\int_{0}^{\ 2\pi} \ |e^{sin(x)}cos(x)| \, dx$$. The original poster expresses uncertainty about the approach to take, particularly regarding how to handle the absolute value within the integral.
The discussion includes affirmations of the proposed method for handling the integral. Participants are exploring the approach without reaching a definitive conclusion or consensus on alternative methods.
There is a mention of the integral simplifying to a specific numerical value, but the focus remains on the method of integration rather than the solution itself. The original poster expresses a desire for potentially less tedious methods, indicating a consideration of efficiency in problem-solving.
physicsdreams said:Homework Statement
$$\int_{0}^{\ 2\pi} \ |e^{sin(x)}cos(x)| \, dx$$
I know that it simplifies to $$ 2e- \frac{2}{e} ≈ 4.7 $$ I'm not sure how to approach this problem. Do I just break the integral up into the domains where it's positive and negative and integrate each component separately as I would with a much simpler absolute value function?
Thanks in advance,
physicsdreams
Dick said:Yes, that's exactly what you should do.
physicsdreams said:Wow, you're quick! Thanks for the help, Dick. I was hoping there would be a less tedious method to go about solving problems such as these, but I guess that's math for ya'.
Thanks again!