You may not use a calculator which has symbolic manipulation capabilities. When answering these questions, please be sure to 1) check answers when possible, 2) clearly indicate your answer and the reasoning used to arrive at that answer (unsupported answers may not receive credit). Each question is followed by space to write your answer. Please lay out your solutions neatly in the space below the question. You are not expected to write each solution next to the statement of the question. 100: use calculus to evaluate the following integrals. 0 cos2 x dx (a) z (b) z x sin(2x) dx (c) z (d) z. 1 + cos2 x (9 x2)3/2 sin x. Do not solve for the constants. (a) (b) 1 (x2 + 1)(x 2)2 x (x2 2x + 1)2: determine if each of the integrals is convergent or divergent and evaluate the convergent improper integrals. (a) z (b) z .