I am struggling with a area between the curves problem. I need to find the area between y=tanx and y=2sinx over the interval

and

.

Since the curves cross at 0 and are symmetrical, I'll just go from

to 0 and double the answer. So I get

I can't get the interval on the integral to work with a fraction and Latex.

Anyway, that yields:

$\displaystyle -\ln(\cos(x))-2\cos(x)$

The answer in the book is $\displaystyle 2+2\ln(2)$, after you multiply by 2 to account for the 2nd half of the interval.

I agree with much of the answer, except that I get $\displaystyle 2+2\ln(\frac{1}{2})$, because $\displaystyle \cos(\frac{\pi}{3})$ (positive or negative) is 1/2.

Anything that I could be doing wrong?