Problem 4: [30 pts] (Evaluating an integral) Reminder: You may use any type of calculator or other technology to draw any necessary graphs or perform any arithmetic calculations, but all other work must be done by hand. Consider the integral / 8 sec4 (22:) tan(2x) dar. A. [10 pts] Use an appropriate usubstitution to evaluate the integral. Hint: If you evaluate the integral correctly, you should nd that / 8 sec4(2m) tan(2:z:) d1: = tan4 (2x)+ 2 tan2(2x) +C'. 7r / 2 B. [20 pts] Morgan is asked to evaluate the integral / 8sec4(2:c) tan(2:c) 03:6 and gives the following argument. 0 Since /8sec4(2:c) tan(2:c) drc = tan4(2:c) +2tan2(2:) + C, I can evaluate the denite integral by using the Fundamental Theorem of Calculus: 7r/2 0 = [tan4 (7r) 2 tan2 (7r)] [tan4 (0) 2 tan2 (0)] = O. f/Q 8sec4(2:c) tan(2:c) d$ = [tan4(2$) 2 tan2(2$)] 0 Determine whether Morgan's argument is correct or incorrect. If their argument is incorrect, make sure to explain What error or errors they made7 then analyze the integral correctly