01:640:151 Final: 01:640:151 - Final Exam
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Exam guide covers the following topics: review of, antiderivatives, areas and distances, the definite integral, the fundamental theorem of calculus. Indefinite integrals: the net change theorem, the substitution rule, areas between curves, volumes, exercise questions. 1 (cid:1858)((cid:1876)) = (cid:1876)9 ((cid:1876)) = (cid:1876)8 + (cid:1829) (cid:1858)((cid:1876)) = 8sin(4(cid:1876)) ((cid:1876)) = 2cos((cid:1876)) + (cid:1829) (cid:1858)((cid:1876)) = 6(cid:1876)2 + 10(cid:1876) + 4. Find an equation satisfying the following conditions ((cid:1876)) = 2(cid:1876)3 + 5(cid:1876)2 + 4(cid:1876) (cid:1858) ((cid:1876)) = 12 2(cid:1876), (cid:1858)(0) = 9 (cid:1858)(2) = 7. Find the most general antiderivative (cid:1858) ((cid:1876)) = (cid:1829) + 12(cid:1876) (cid:1876)2 (cid:1876)3 (cid:1858)((cid:1876)) = (cid:1830) + (cid:1829)(cid:1876) + 6(cid:1876)2. Applying the first initial condition (cid:1858)(0) = 9. 9 = (cid:1830) + (0)(cid:1829) + 6(0)2 . Applying the second initial condition (cid:1858)(2) = 7. 7 = 9 + (2)(cid:1829) + 6(2)2 2. (cid:1829) = (cid:1876)3 (cid:1858)((cid:1876)) = 9 (cid:1876) + 6(cid:1876)2 . Therefore an equation that satisfies these conditions is.
