Work out the following calculus problems. Show workings for each one. Thank you 1. Find f 1%: air. Show workings. 2, If [(0) = l. f(1) = 2.f'(0) = l and f'(]) = 2.what is]1 (1'+1)f"(.r)d1".' u Show workings. 3 Let a, b be real numbers and consider the integral (ax+ b) cos(x) dx. Using integration by parts will lead to which of the Show workings. following expressions? . A. (ax + b) cos(x) + 2a / xsin(x) dx . B. 2axcos(x) +2 /(ax +b) sin(x) dx . C. (ax + b) sin(x) - 2a ( xsin(x) dx . D. (ax + b) cos(x) - 2a / xcos(x) dx . E. 2arsin(x) -2 /(ax +b) sin(x) dx 4, Show workings. Find w2 In(w) dw. A. w3 In(w) + C B. In(w) 42 - 1+C C. w + C 202 - 1+C D. In(w) 43 - E. In(w) 2 - w2 + C5 . Select the answer that is equal to / ex/2f(x) dx. Show workings. A. 20 * /2 f (z ) + 2 /2f'(x) dx B. er /2 f (z) - ehf'(x) dx C. 20*/2 f (x) - 2 "/2f'(x) dx D. "/2 f (x) - 2 /2f'(x) dx