The function f(t), defined as is shown in the plot below. f(t) f(t) The function F(x)...

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The function f(t), defined as is shown in the plot below. f(t) f(t) The function F(x) is defined as 10- -5- 2t, 5-², -4, 4t - 36, 5 −1≤t<+2 +2 ≤ t < +6 +6 < t < +8 +8 ≤t 10 F(x) = f*, f(t) dt. 15 t (a) Evaluate F(0). (b) What feature of the graph above does the value of F(0) correspond to? (c) Express F(b) – F(a) as a single integral. Hence, explain how you could evaluate the expression F(8) - F(6) without evaluating any integrals. (d) Complete the following table: X -1 0 26 8 10 12 F(x) (e) In terms of the plot of y = f(t) above, what would it mean for F(x) = 0 for x‡ -1? (f) Find the four values of x for which F(x) = 0. The function f(t), defined as is shown in the plot below. f(t) f(t) The function F(x) is defined as 10- -5- 2t, 5-², -4, 4t - 36, 5 −1≤t<+2 +2 ≤ t < +6 +6 < t < +8 +8 ≤t 10 F(x) = f*, f(t) dt. 15 t (a) Evaluate F(0). (b) What feature of the graph above does the value of F(0) correspond to? (c) Express F(b) – F(a) as a single integral. Hence, explain how you could evaluate the expression F(8) - F(6) without evaluating any integrals. (d) Complete the following table: X -1 0 26 8 10 12 F(x) (e) In terms of the plot of y = f(t) above, what would it mean for F(x) = 0 for x‡ -1? (f) Find the four values of x for which F(x) = 0.