Introduction to Maple Activities and QuestionsMaple is a computer algebra system, which was first developed in 1980 out of the University of Waterloo in Canada.Goal: Maple can handle numerical, symbolic, and graphical representations. Exploring these representations is one of the course goals of Calculus and Analytic Geometry II, as is an introduction to this kind of software to get acclimated with its benefits, and use it to help us make connections to the work we are doing by-hand. Calculus II offers many opportunities for creative problem solving. One goal of group work and interactions in class and lab is to help you practice and get used to productive failures (where you understand and correct mistakes) so that you can become independent and successful yourself.So engage with the material and your neighbors as you write your responses on a piece of paper. In the following, execute the command code by hitting return on each red line, as you read and answer questions.Maple knows all the basic techniques of integration that we are supposed to learn, including substitution, integration by parts and much more. Maple applies these techniques without telling us which one it is using and comes up with a final answer, when it can.Int displays the integral while int computes it. Question 1: Is the following a substitution, parts, or neither? (go to the red line and enter return to execute the command and use it to help you)Int(x^3*ln(x),x); int(x^3*ln(x),x);Please note that it should be + c at the end, but Maple leaves that off!Question 2: If the above integral is integration by subsitution, write down w, dw, and the integral with respect to w. If it is integration by parts, write down u, u', v, v', and uv - integral u'v dx.Visualization of the definite integralMaple can also compute the definite integral:Int(x^3*ln(x),x=0..1); int(x^3*ln(x),x=0..1);We can also plot the function, and see the geometric representation of the area under the curve that Maple just solved for to see why Maple gives a negative response: plot(x^3*ln(x),x=0..1);Question 3: Is the following a substitution, parts, or neither? Int(x^2*sin(x^3)*cos(x^3),x); int(x^2*sin(x^3)*cos(x^3),x);Question 4: If the above integral is integration by subsitution, write down w, dw, and the integral with respect to w. If it is integration by parts, write down u, u', v, v', and uv - integral u'v dx.Question 5: The following integral is quite important in statistics and other real-life applications such as for harmonic oscillators. It is known as the Euler\342\200\223Poisson integral or the Gaussian integral. This is not an elementary integral. Write down what Maple outputs for the integral?Int(exp(-x^2),x); int(exp(-x^2),x);If you search for erf(x) on the internet you would notice that it is defined as a constant times the integral, so the integral has erf in it and erf has the integral in it, i.e. not all that revealing. To find more information about it, Maple can approximate integrals it can not compute directly by Riemann sum approximations (like you did in Calculus I) or by Taylor series, both of which we will be exploring this semester.. Execute the following and notice the rectangles that have width LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEoJiM5MTY7eEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYyRjw=and height as the function value. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbW9HRiQ2MFEmJmludDtGJy8lK2ZvcmVncm91bmRHUS5bMTQ0LDE0NCwxNDRdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSy1JI21pR0YkNiZRImZGJy8lJ2l0YWxpY0dRJXRydWVGJ0YyL0Y2USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYoLUZPNiZRInhGJ0ZSRjJGVS9GMFEqWzAsMCwyNTVdRidGMi8lKXJlYWRvbmx5R0ZULyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RidGNUYyRjUtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuM2VtRicvJSZkZXB0aEdGZW8vJSpsaW5lYnJlYWtHUSVhdXRvRictRiw2MFEwJkRpZmZlcmVudGlhbEQ7RidGL0YyRjVGOEY7Rj1GP0ZBRkNGRUZHRklGTEZmbi1GLDYuUSJ+RidGMkY1RjtGPUY/RkFGQ0ZFRkdGSUZMRmluRjJGW29GXW9GNQ== arises as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEoJiM5MTY7eEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYvRjJGNQ==goes to 0 and we get better approximations that approach the integral. with(Student[Calculus1]): ApproximateInt(exp(-x^2),x = 0 .. 2, output = plot); Next go back to the class highlights page and follow the instructions there.