# The area between the curves y=tanx and y=2sinx, -pi/3

8 years ago
tanx=2sin(x) gives , -pi/3 and pi/3 as point of intersection between -pi/3 and pi/3

$\int_0^{\frac{\pi }{3}} (\tan (x)-2 \sin (x)) \, dx+\int_{-\frac{\pi }{3}}^0 (\tan (x)-2 \sin (x)) \, dx=-1+\log (2)+1-\log (2)=0$