# _____ Mr. Corraliza Mathematica Lab #1 Objective: you will learn some basic features of Mathematica which are relevant to a general

MAT 282 Name: ___________ Mr. Corraliza Mathematica Lab #1 Objective: you will learn some basic features of Mathematica which are relevant to a general study of Calculus. Upload the final project on D2L as a pdf. You can save the file from Mathematica as a Pdf. Important: Whenever you multiply two quantities, you need to use the symbol *. So, 3x is written 3*x. To make a calculation or graph in Mathematica, you need to hold down the “Shift” key when you type Enter! Introduction: 1.) Mathematica will allow you to take derivatives and integrals of functions. It can use the Product, Chain and Quotient Rules, as well as techniques of integration such as Integration by Parts. Ex: Let f(x) = x2 cos(3x). Find ?f(x) dxand f ‘ (x) Note: In calculus, the “Plus C” for indefinite integrals is not optional. However, Mathematica does not indicate the existence of the constant! Syntax Note: Cosine is “Cos” (capitalized). To plug 3x into cosine, you use square brackets. Also: To make a calculation or a graph, you need to hold down the “Shift” key when you type “Enter”! 2.)Notice the syntax for “square root”: x dx is: 3.) You can graph regular 2-space graphs using Mathematica, including relations that are implicitly defined. Ex: Graph y = x3 – 9×2 + x – 4 (Use the “Plot” function) Ex2: Graph x2 + 4y2 = 4 (Use the “ContourPlot” function) Ex3 Graph y = -4Cos(3x)^2 and y = -7 (Use “Plot”, function) with PlotLegends->”Expressions”] Plot[{-4Cos[3x]^2, 7},{x,0,Pi}, PlotLegends->”Expressions”] Syntax Notes: For implicitly defined relations, you need to type two equals signs! Ex3: Graph r = sin(3?) (Use the “PolarPlot” function) Ex4: Graph x=cos(3t), y=sin(2t) (Use the “ParametricPlot” function) ++++++++++++++++++++++++++++ Your assignment is on the next page Mathematica Lab ONE Do the following, and clearly show me the Mathematica syntax (so I know you used Mathematica) Use screen clippings or copy-paste the images, as I did in the previous pages. 1.)Evaluate the following integrals: 1a.) ! !(!”!!) dx 1b.) ! !!! dx 2.) Graph the following: 2a.)2sin(xy) = x – y on [-10,10]x[-10,10] 2b.)8sin(xy) = x – y on [-10,10]x[-10,10] 3. Sketch the region and find the area of the triangle with vertices (2,0), (0,2),(-1,1). Use the function Graphics[Line[ {{p1},{p2},{p3}, etc}]] Example find equation of a line point (5,2),(1,3) To find the equation of the line use Solve[y-2==(2-3)/(5-1)*(x-5),y)] This will give you the equation of a line. Output is {{? ? !”!! ! }} Use that equation to integrate and find the area. Find there intersections using NSolve[{eq1,eq2},{x,y},Reals] This will output the intersections and you can use that for your limits of integration. Give the solution to the area under the curve. Do not manually add them together, use Mathematica 4. Graph the function and then using the method of Disks/Washers. Find the volume of rotation for ? = ???! ? , ? = 0, 0 = ? = ? ????? ? = -1 5. Graph the function and then using the method of Disks/Washers. Find the volume of rotation for? = ?, ? = ?? !!! !, ????? ? = 3. Use NSolve to find the points of intersection 6. Graph the function and then using the method of Cylindrical Shells Find the volume of rotation for ? = ???! ? , ? = ???! ? , 0 = ? = ?, ????? ? = !! ! . When graphing using ContourPlot and use -? = ? = ? and 0 Save your final project as a pdf, this can be done from Mathematica. Then upload the pdf to D2L.