1. CHAPTER 2 2.4 Continuity Areas Between Curves The area A of the region bounded by the curves y = f(x), y = g(x), and the lines x = a, x = b, where f and g are continuous and f(x)  g(x) for all x in [a,b], is A =  a b [ f (x) - g(x)] dx. A = lim n ->   i=1 n [ f(x i * ) - g(x i * )]  x

2. Example: Find the area of the region between. y = x 2, y 2 = x. Example: Find the area of the region between. y = cos x, y = sec x, x = -  /4, x =  /4. Example: Find the area of the region between. y =1/x, x = 0, y = 1, y = 2.

3. CHAPTER 2 2.4 Continuity Example: Estimate the area of the region enclosed by the loop of the curve x=t 3 –12t, y=3t 2 +2t+5. Example: Graph the parametric curve x = t – 1/t, y = t + 1/t. Find the area enclosed between this curve and the line y = 2.5. Areas Enclosed by parametric curves A =  a b y dx =    g(t) f’(t) dt or [    g(t) f’(t) dt