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I. Multiple Choice List your answers on the back of the exam in the provided grid. 1. Calculate without calculator the exact value of the following definite integral. ∫ 2 2???? ????+5????????. A. 2????7 − 2????5 B. 2????7 C. ???? 7 - ???? 5 D. 1896.43999 E. None of these. 2 2 2 ∫ 2????????+5???????? = 2????????+5 2 = 2????7 − 2????5 0 2. Calculate without calculator the exact value of the following definite integral. ∫ 3 4 ????????. 1 ???? A. − 32 9 B. 4.39444 C. ln 12 D. 4 ln 3 E. None of these ∫ 3 4 ???????? = 4 ln ???? 3 = 4 ln 3 − 4 ln 1 = 4 ln 3 since ln 1 = 0 1 ???? 1 3. Decide whether or not the given integral converges. ∞ 8 ∫ ???? 2 ???????? If it converges determine the value it converges to. A. 8 3 B. Diverges C. 8 D. 4 E. None of these ∞ 8 ???? 8 −8 ???? 8 ∫ 2 ???????? = lim ∫ 2 ???????? = lim(( ) ) = lim(− + 8) = 8 1 ???? ????→∞ 1 ???? ????→∞
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