For each of the following functions, graph the region bounded by the functions,

Question

For each of the following functions, graph the region bounded by the functions, and find the area of the region. You will need to find the regions of intersection first, and then decide which function is greater than the other in each region of integration. f(x) = x^3-2x+1 g(x) = -2x x = 1 f(x) = sin (x) g(x) = cos(2x) -pi/2 x 5 pi/6 f(x) = ln(x) g(x) = e-x 0 x 3 For this problem, make sure that you use the EVALF command in order to simplify your integration limits Consider that two particles are traveling the paths of the following functions: f(x) = 3/4x2 - x + 1 g(x) = -x2 + 2x +3 If each particle is to begin at one point of intersection at the same time and travel to the other point of intersection (at the same velocities), then which particle would arrive first? WHY? (hint: section 6.3) Tip: Plot these functions on the same set of axes from x= -1 to x= 3.

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