7.4 Partial Fractions and Trig Substitution in Mapleby Dr. SarahMaple is a computer algebra system, which was first developed in 1980 out of the at the University of Waterloo in Canada.Maple can handle numerical, symbolic, and graphical representations. Exploring these representations and an exposure to this type of technology are course goals of Calc II.Respond to the following questions in your notes:Example 1: Number 2 on Partial Fractions Group Work Target PracticeTake out your 7.4 Partial Fractions Group Work Target Practice from the last class. In the following example, read through and execute the command code by hitting return at the end of the line. Compare with your by-hand work on #2.num2:=(3*x+11)/(x^2-x-6);Maple's convert feature factors the demonimator into parts and solves for the constants in the partial fractions:convert(num2, parfrac, x);Maple's int feature integrates the function without specifying that it does it by partial fractions, although the natural logs in the output does give you a clue that it was via partial fractions.Int(num2,x); int(num2,x); Please note that it should be +c at the end, but Maple leaves that off!Question 1: Aside from the +c, does Maple's work match your by-hand work?Example 2: Trig SubstitutionExecute the following:Int(x^2/(sqrt(1-x^2)),x);Question 2: Why doesn't regular w-sub work here?
Question 3: What trig sub should we use here? x =
Question 4: Why is that the correct trig sub to use? Maple's int feature integrates the function without specifying that it does it by trig substitution, although the square root and the trig function in the output does give you a clue that it was via trig sub--execute to see this: int(x^2/(sqrt(1-x^2)),x);