substiution
Homework: Trig p. 494495: Reccommended: 430, 3341. Required: 10, 14, 18, 20, 22, 26, 28, 30 Due: Friday, 20 May 2005 The following table is very useful: Expression Identity Substitution
2 2 1 - sin2 () = cos2 () x = a sin(), -/2 /2 a - x 2 2 1 + tan2 () = sec2 () x = a tan(), -/2 < < /2 a + x 2 - a2 x sec2 () - 1 = tan2 () x = a sec(), 0 < /2 or < 3/2 It is a good exercise to see if you can rederive this whole table from scratch. you If can do that, you will learn it without memorization. Yesterday's example (up to the point where I stopped):
et
9 - e2t dt
=
et
9 - (et )2 dt
(Let u = et , du = et dt.) = 9 - u2 du (Let u = 3 sin(), du = 3 cos()d) = = = = = = 9 9 9 9 - 9 sin2 ()3 cos()d 9(1 - sin2 ())...