Sketch the region enclosed by the given curves.
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

Answers

Answered by Steve
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)
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