4. (a) (10 marks) Let f be integrable on [a, b]. Suppose ceR and g: (a + c,b+c] → R such that == g(2) = f(:1 - c), E (a

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4 A 10 Marks Let F Be Integrable On A B Suppose Cer And G A C B C R Such That G 2 F 1 C E A 1 (45.7 KiB) Viewed 21 times

4. (a) (10 marks) Let f be integrable on [a, b]. Suppose ceR and g: (a + c,b+c] → R such that == g(2) = f(:1 - c), E (a +c,b+c] x I + Prove that g is integrable on [a +c,b+c] and pbtc ļi rede f(c) dr g(2) dar atc (b) (20 marks) Let h: R+R be integrable on every bounded interval and h(x + y) = h(2) +h(y) for any X,Y ER Show that h(-2) = ct for any I ER, where c=h(1). (Hint: Fix any I,Y ER and integrate h(t+y)=h(t) +h(y) with respect to t on (0, 3). Then use (a).) =