Definite Integral of Absolute Value Function (Calc I)

[physicsdreams]

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]

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

Yes, that's exactly what you should do.

 

[physicsdreams]

Yes, that's exactly what you should do.

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!

 

[Dick]

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!

Well, it was a pretty easy answer. You're very welcome.