Question

Test: Final This Question: 6 pts Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. XX Which substitution transforms the given integral into one that can be evaluated directly in terms of 0 OA. X 3 tano OB. X= 3 sino OC. X= 3 sec 0 Given the expression for x above, find dx in terms of O and do. dx = 00 dx x4-9 Click to select your answer(s).

Answer 1

I= Put x = x= 3 seco dx= 3Seco tano de x3 g = a sec²0-9= 9 (Sec²0-)) -a tanzo S v se za 3 tano I= 3 seco tano do 3Seco (3 tano) I = O+G 3 x = 3Seco y 0 = Sec! ( ) I = I Sect 3 oltc 3

Answer 2

ANSWER :

Substitution : Option C :  x = 3 sec θ. (ANSWER)

=> dx = 3 sec θ tan θ dθ  (ANSWER)

∫ dx / (x sqrt(x^2 - 9)) 

Using the above substitution , the given integral is :

=  ∫  3 sec θ tan θ dθ / (3 sec θ * sqrt (9 sec^2 θ - 9) )

= ∫ 3 sec θ tan θ dθ / (3 sec θ * 3 tan θ)

= ∫ dθ/3

= θ/3 + C 

= 1/3 * sec ^(-1) (x/3) + C      (ANSWER).