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Homework 2 – due February 5th You only need to hand in homework problems 1 and 2. The practice problems are optional. Homework Problems 1. Find the volume obtained by rotating the region between y = sin(x) and y = cos(x) from x = x = π around the line y = 2. Hint: cos(x)2 − sin(x)2 = cos(2x) 2. Define Z x2 (x − t) sin2 (t) dt. G(x) = 1 Find G0 (x), the derivative of G(x). Practice problems 1. Let f (x) be a continuous function on [0, 5] such that f (x) + f (x − 1) = Find R2 0 q √ x + 1. f (x) dx. 2. Let f (x) be a continuous function. Define R1 f (x − t) dt and 0 R x2 (b) G(x) = x f (xt) dt, x > 0. (a) G(x) = In each case find the derivative G0 (x). 3. Let f (x) be a continuous functions which satisfies the following equation e R x−1 0 f (t) dt Z + sin 0 for every real number x. Find f (0). 1 x−1 2 f (t) dt = ex π 2 to