-> 4. (a) (10 marks) Let f be integrable on (a, b). Suppose ce R and g: [a+b+c] + R such that g(x) = f(r-c), re la + cb+

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4 A 10 Marks Let F Be Integrable On A B Suppose Ce R And G A B C R Such That G X F R C Re La Cb 1 (21.55 KiB) Viewed 26 times

-> 4. (a) (10 marks) Let f be integrable on (a, b). Suppose ce R and g: [a+b+c] + R such that g(x) = f(r-c), re la + cb+c] Prove that g is integrable on (a + c, b + c and fx) (r) dx = L*9(e) de btc gr = (b) (20 marks) Let h: R+R be integrable on every bounded interval and h(x + y) = h(x) +h(y) for any 1,YER Show that h(x) = cr for any reR, where e=h(1). (Hint: Fix any , Y ER and integrate h(t + y) =h(t) +h(y) with respect to t on (0,r). Then use (a).)