Sketch the region enclosed by the given curves.

Question

y = tan 3x, y = 2 sin 3x, −π/9 ≤ x ≤ π/9
then then find the area.
i can sketch but cant find correct area

Answer 1

algebraically, since both functions are symmetric about the origin, the area is zero.

geometrically, using symmetry, you have the area is

2∫[0,pi/9] (tan3x - 2sin3x) dx
= 2/3 (2cos 3x - log cos 3x)[0,pi/9]
= 2/3 (log2 - 1)