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Unformatted text preview: THE INTERNATIONAL UNIVERSITY(IU) - VIETNAM NATIONAL UNIVERSITY HCMC FINAL EXAMINATION 26 June 2009 • Duration: 120 minutes SUBJECT: CALCULUS I Head of Dept of Mathematics Lecturers: Prof. DrSc. Phan Quoc Khanh N.V.Thu, N.Dinh, N.N.Hai, J.C.Harris, M.D.Thanh INSTRUCTIONS: Answer ALL questions in Section A and any TWO questions in Section B. Calculators and dictionaries allowed. All other documents prohibited. SECTION A A1. [10 marks] Evaluate the following integrals: ( a ) Z x sin xdx, ( b ) Z x + 5 ( x- 1)( x + 2) dx. A2. [4 marks] If f is continuous on [ a, b ], show that 2 Z b a f ( x ) f ( x ) dx = [ f ( b )] 2- [ f ( a )] 2 . A3. [8 marks] State whether the following statements are true or false. If false, give an explanation or a counterexample. (If true, no explanation is required.) (a) If f is continuous and positive on [ a, b ] then R b a f ( x ) dx > 0. (b) If f is continuous on [ a, b ] and R b a f ( x ) dx > 0 then f ( x ) > 0 for all x on [ a, b ]....
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