The region bounded by the given and find the area of the region
The sketch of the region
Area is the integral of the difference of two functions.
y=tanx, y=2sinx , -π3≤x≤π3 Since the area is symmetric about origin
By solving integral,
By substituting limits,
But ln1/2 = ln(2)-1 = -ln2 Thus by simplifying,
The sketch of the region: