Calc 2 Quiz 1 Solutions - Quiz#1 Solutions Problem 1...

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Quiz #1 Solutions Problem # 1 Function 𝐴(?) is given by formula 𝐴(?) = ∫(5 − 3?)?? 𝑥 3 a) graph ? = 𝐴(?) ??? 3 ≤ ? ≤ 10 b) calculate the values of 𝐴(3), 𝐴(5) ??? 𝐴(9) 𝐴(3) = ∫(5 − 3?)?? 3 3 = 0 𝐴(5) = ∫(5 − 3?)?? 5 3 = [5? − 3 2 ? 2 ] (???? 3 ?? 5) = (25 − 3 2 ∗ 25) − (5 ∗ 3 − 3 2 ∗ 9) = −14 𝐴(9) = ∫(5 − 3?)?? 9 3 = [5? − 3 2 ? 2 ] (???? 3 ?? 9) = (45 − 3 2 ∗ 81) − (5 ∗ 3 − 3 2 ∗ 9) = −78 c) calculate the values of 𝐴 (3), 𝐴 (5) ??? 𝐴 (9) 𝐴 (3) = (5 − 3 ∗ 3) = 5 − 9 = −4 𝐴 (5) = (5 − 3 ∗ 5) = −10 𝐴 (9) = (5 − 3 ∗ 9) = −22 Problem # 2 Find the exact area under one arch of the cosine curve ∫ 5 cos(?)?? 𝜋 2 𝜋 2 = 5 ∫ cos(?)?? 𝜋 2 𝜋 2 = 5 (sin ( 𝜋 2 ) − sin (− 𝜋 2 )) = 5(1 + 1) = 10
Problem # 3 Use the Fundamental Theorem to evaluate the definite integrals (simplify your answer, but do not approximate)

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