Solução_Calculo_Stewart_6e

F.
348 ¤ CHAPTER 7 TECHNIQUES OF INTEGRATION
TX.10
(b) Let u = a sin θ ⇒ du = a cos θdθ, a 2 − u 2 = a 2 1 − sin 2 θ = a 2 cos 2 θ.
√
a2 − u 2 a 2 cos 2
θ 1 − sin 2
du =
u 2 a 2 sin 2 θ dθ = θ
sin 2 θ
√
a2 − u
= −
2 u
− sin −1 + C
u
a
dθ = (csc 2 θ − 1) dθ = − cot θ − θ + C
61. For n ≥ 0, ∞
0
x n dx = lim
t→∞
x n+1 /(n +1) t
0 = ∞. Forn