15 - 8 2. 5.3.18 Area functions for the same linear function 7 Let f(t) = 2t - 2 and consider the two area functions 36 - 12 24 - 8 A(x) = / f(t) dt and F(x) = / f(t)dt. IC 4 (a) Evaluate A(2) and A(3). Then use geometry to find an expression for A(x), for x 2 1. A(2 ) = 1 A ( 3 ) = 4 (b) Evaluate F(5) and F(6). Then use geometry to find an expression for F(x), for x 2 4. (5) = 7 F(6) = 14 (c) Show that A(x) - F(x) is a constant and that A'(x) = F'(x) = f(x)