4 A 10 Marks Let F Be Integrable On A B Suppose Ce R And 9 A C B C R Such That G X F Z C C A C 1 (31.12 KiB) Viewed 19 times
please complete, especially 4b
4. (a) (10 marks) Let f be integrable on [a, b]. Suppose ce R and 9: (a + c,b+c] + R such that g(x) = f(z - c), c + {a+c, bạc Prove that g is integrable on (a + c, b + c) and I saw) dx = CS f) = b+c g(2) de (b) (20 marks) Let h: R+R be integrable on every bounded interval and h(x + y) = h(x) +h(y) for any x, y ER Show that h(c) = cr for any r ER, where c=h(1). (Hint: Fix any r, y ER and integrate h(t + y) = h(t) +h(y) with respect to t on (0, 2). Then use (a).)
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