Final Practice Q2 - Looking for a detailed worked solution with theoretical explanation

This question has several parts. Please scroll down and try to answer all sub-questions until you get to "END OF THIS QUESTION". For the questions below, you will need to use Maple syntax for expressions: Expression How to enter + 2 + + 2 + V1-2t to (-2) + to2 + sqrt ( 1 - 2* t) / (4+5*t*3) 4+5+3 405t 4* exp (5*t) Int = logt = loge t In (t) sint, cost, tant, sect, csetsin (t), cos (t) , tan (t) , sec(t) , csc(t) sin t, cost, tan It arcsin (t), arccos (t), arctan(t) Note: the parentheses ( ) must be present in the evaluation of functions, even if just evaluating at t. For instance, it is sin (t) , not sin t. Note that you must enter exact answers, for example, for 1/3 do not enter a decimal approximation such as 0.3333333333. For negative denominators you must use brackets, for example, -3/2 or 3/ (-2) but not 3/-2. Enter Pi and exp (1) for 7 and the Euler number e. You are given the integral 912 - 16 - dx. 31 In order to compute this integral, we will attempt to use the substitution I = =sect. a) We start by noting that da = f(t) dt, where f (t) = (enter your answer in valid maple syntax) b) Hence, the integral can be written in the form I = / 9(t) at. Type the expression for g in the box below. g (t) = (enter your answer in valid maple syntax) c) The computation of the integral above results in I = 4/3 tan(t) - 4/3t. In order to write this expression in terms of , 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 a and it is given to you that one of these is equal to 3x. The length of the third remaining side is a constant integer. Find this integer and write it in the box below: Number END OF THIS