Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 288: 58

$0.093924$

The area between the two curves over an interval $[m,n]$ about the x-axis is given by: $Area, A= \int_{0}^{0.67} (\sin x - \tan^2 x ) \ dx \\ = [\cos x ]_0^{0.67} -[\tan x-x]_{0}^{0.67} \\=\cos (0.67) - \tan (0.67)-0.67$ Now, we will use a graphing calculator to obtain the approximate value of the area. So, $Area, A \approx 0.093924$