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Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the indefinite integral fmg (4 + 43:4)9 dx Then the most appropriate substitution to simplify this integral is U = Then dz = f(z) du where =) = After making the substitution we obtain the integral [ g(u) du where g(w) =[ | This last integral is: = D +C (Leave out constant of integration from your answer.) After substituting back for u we obtain the following final form of the answer: = |+c (Leave out constant of integration from your answer.) \fMatch each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. A. tan(0) where x = 8 sin 0 B. cos (0) where x = 8 sin 0 C. (1/2) sin(20) where x = 8 sin D. sin(0) where x = 8 tan 0 E. cos (0) where x = 8 tan 0 V64 + 22 2. /64 - 42 3. V 64 - 12 64 4. V64 + 2 2 V64 - 22 5. 8For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS. A. x = 2 tand B. x = 2 sin 0 C. x = 2 sec 0 4+ x2 da 2 . x2 - 4 dx 3. (x2 - 4) 5/2 dx 4. (4+ 22) 3 5.Using the method of u-substitution, /:(5:6 6)'dx = /: f(u) du where U= (enter a function of x) du = dzx (enter a function of ) a = (enter a number) b= (enter a number) flu) = E] (enter a function of u). The value of the original integral is D Note: You can earn full credit if the last answer box is correct and all other answer boxes are either blank or correct. \f