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Unformatted text preview: xc ) r on [ c,c + d ]. Here c, d, r are constants. Answer: d r r + 1 3 5.4 Mean Value Theorem for Deﬁnite Integrals If the function f is continuous on [ a,b ] the property of the deﬁnite integrals: 6 Z b a f ( x ) dx 6 guarantees that 6 f av 6 Recall that the Mean Value Theorem for continuous function states that f attains any value between its maximum and minimum. In other words: This proves the following theorem: Theorem Mean Value Theorem for Deﬁnite Integrals If f is on [ a,b ], then there exists at least one point x ? inside [ a,b ], such that: Example 4 Find the point(s) x ? that satisfy the conclusion of the Mean Value Theorem for the following functions: • f ( x ) = x 21 on [1 , 1] 4 • f ( x ) = (2 x3) 3 on [1 , 4] • To do f ( x ) = 1 x , on [1 , 3]...
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This note was uploaded on 10/02/2011 for the course MATH 1206 taught by Professor Llhanks during the Fall '08 term at Virginia Tech.
 Fall '08
 LLHanks

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