Test 1 will cover Ch. 6: sections 1, 2, 3, 5, Ch. 7: sections 1, 2, 3. Things you'll need to know and know how to do for Test#1: Area between 2 curves. Volume = integral of cross-sectional area. Volumes of solids of revolution: by washers and shells. Integration by parts I(rs) = rS - I(r'S), where S'=s and I means integral. Integrals of trig function combos: You'll need to memorize all of the following (please try!): sin2 + cos2 = 1 sin2 x = (1-cos2x)/2 cos2 x = (1+cos2x)/2 2 sin x cos x = sin 2x sec2 = 1 + tan2 Using ' to mean derivative: exp' = exp sin' = cos cos' = -sin tan' = sec2 sec' = sec.tan sinh' = cosh cosh' = sinh Using ^ to mean antiderivative: tan^ = ln|sec| + C sec^ = ln|sec+tan| + C Substitutions for integrating sinmcosn and tanmsecn. Trig substitutions for integrations involving square roots of a2-x2, a2+x2, x2-a2.For the Tests, you may use a non-programmable non-graphing scientific calculator such as the
which can be bought for $10 or less.Note: sinh, cosh, tanh, etc. are on your calculator! See this.
