Trigonometric substitution

Problem 2: Indicate the appropriate trigonometric substitution that you should use to evaluate the following integrals: It* = >x = tang Integral a = 1 - X2 = ) x = sine 1 x 7 4X + 11 = (X+2) 7 7 x 2 1 = > X = Sece dx 2 + 40 +11 x = a s in G = > vaz x 2 1 dx x2 V1 - x2 sine X = a tanG = > Vaz+ x2 1 dx X= asec G = >v x292 V ( 2 + 1)2 - 4 dx (9x2 - 1) 3/2 Page 1 of 6C Math 1132 Exam 1 - 412 Problem 3: For each trigonometric substitution listed below, give an example of one integral that you would evaluate using the given substitution: Substitution Example Integral = sec 0 x = 3 sin 0 x = 2 tan 0 x = 4tan 0 + 1 Problem 4: Indicate the appropriate form for the partial fraction decomposition that should be used to evaluate the following integrals (Note: Do not find the values of the parameters):Problem 5: Suppose we use the trig substitution x = 5 tan(0) to evaluate an integral. After integrating, we get the solution sec(0) + C. How can we rewrite this to be in terms of a? ( A) (B) V 25 + 2 2 5 + C + C V25 - 22 5 (C) + C 25 + 202 ( D) 25 + 2 2 5 + C (E) + C 5x V25 - x2 Page 2 of 6