(1 point) Suppose that F ' (t) = tcos(t) and F (0) = 5. Use the data and method from example 5 in the text to estimate each of the following. F (0.3) = F (0.5) = Example 5 Suppose F' (t) = tcost and F(0) = 2. Find F(b) at the points b = 0, 0.1, 0.2, ..., 1.0. Solution We apply the Fundamental Theorem with f (t) = tcost and a = 0 to get values for F(b): b b F(b) - F(0) = F'(t) dt = t cost dt. o Since F(0) = 2, we have b F (b) = 2+ t cost dt. o Calculating the definite integral fo t cost dt numerically for b = 0, 0.1, 0.2, ..., 1.0 gives the values for F in Table 6.1. Table 6.1 Approximate values for F b 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 F(b) 2.000 2.005 2.020 2.044 2.077 2.117 2.164 2.216 2.271 2.327 2.382 Notice that F(b) appears to be increasing between b = 0 and b = 1. This could have been predicted from the fact that t cost, the derivative of F(t), is positive for t between 0 and 1