You are given the integral 64x2 - 81 dr. I = 6x In order to compute this integral, we may attack this using the substitution a = sec t. a) We start by noting that da = f(t) dt, where %3D f(t) = (enter your answer in valid maple syntax) b) Consequently, the integral can be written in the form I= [olt) dt. g(t) c Type the expression for g in the box below. 9 (t) %3D (enter your answer in valid maple syntax) c) The computation of the integral above results in I = 3/2 tan(t)- 3/2t. In order to write this expression in terms of x, it is convenient to draw a right triangle where t represents one of the acute angles. The lengths of two sides of this triangle are non-constant functions of x and it is given to you that one of these is equal to 8x. The length of the third remaining side is a constant integer. Find this integer and write it in the box below: Number