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Since f(x) is continuous, by the Intermediate Value Theorem it takes every possible value between m and M In particular, there is atleast one place c at which the function f(x) hasa value equal to f(c) = ∫b a f(x)dx b a Multiplying bothsides by b a proves the result 4The first fundamental theorem of integral calculusChapter 5 Integrability on R 51 The Riemann Integral Partition, Upper and Lower Sums De nition 51 Let a;b2R and aA) Since ej p 2 n x n =ej 2 p 4 n x n then DFT ej p 2 n x n =X k1 4 = 1 j,0,1j,1 b) In this case y n =Å1ÅÅÅ 2 ej 2 p 4 n x n ÅÅ1ÅÅ 2 ej 2 p 4 n x n and therefore its DFT is Å1ÅÅÅ 2 X k1 4 Å1ÅÅÅ 2 X k 1 4 =Å1ÅÅÅ 2 1 j,0,1j,1 ÅÅ1ÅÅ 2 2 ƒŒƒfƒB[ƒX ‰Âˆ¤‚¢ ƒXƒj[ƒJ[