// Numbas version: finer_feedback_settings
{"name": "Maria's copy of Integration: Calculating the area under a curve. Needs integration by parts.", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"plotgraph": {"parameters": [["q", "number"], ["x1", "number"], ["x2", "number"], ["ymin", "number"], ["ymax", "number"], ["a", "number"], ["b", "number"], ["c", "number"]], "type": "html", "language": "javascript", "definition": "// Shading under a graph! This functions plots a graph of y = a(x-r1)(x-r2)\n// It creates the board, sets it up, then returns an\n// HTML div tag containing the board.\n\n\n// Max and min x and y values for the axis.\nvar xmin = -1;\nvar xmax = 7;\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '500px',\n  '500px',\n {\n   boundingBox: [xmin,ymax,xmax,ymin],\n   axis: false,\n   showNavigation: false,\n   grid: true\n }\n);\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar brd = div.board; \n\n// create the x-axis.\nvar xaxis = brd.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = brd.create('ticks',[xaxis,1],{\n  drawLabels: true,\n  label: {offset: [-4, -10]},\n  minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = brd.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nyticks = brd.create('ticks',[yaxis,5],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 4\n});\n\n\n\n// This function shades in the area below the graph of f\n// between the x values x1 and x2\n\nvar shade = function(f,x1,x2,colour) {\n  var dataX1 = [x1,x1];\n  var dataY1 = [0,f(x1)];\n\n  var dataX2 = [];\n  var dataY2 = [];\n  for (var i = x1; i <= x2; i = i+0.1) {\n      dataX2.push(i);\n      dataY2.push(f(i));\n  }\n\n  var dataX3 = [x2,x2];\n  var dataY3 = [f(x2),0];\n\n  dataX = dataX1.concat(dataX2).concat(dataX3);\n  dataY = dataY1.concat(dataY2).concat(dataY3);\n\nvar shading =  brd.create('curve', [dataX,dataY],{strokeWidth:0, fillColor:colour, fillOpacity:0.2});\n\nreturn shading;\n}\n\n\n//Define your functions\nvar f1 = function(x) {\n  return x*Math.exp(a*x);\n}\n\nvar f2 = function(x) {\n  return a*x*x + c;\n}\n\n\n\n//Plot the graph and do shading\nswitch(q) {\n    case 1:\n        brd.create('functiongraph', [f1]);\n        shade(f1,x1,x2, 'red');\n        break;\n    case 2:\n        brd.create('functiongraph', [f2]);\n        shade(f2,x1,x2,'red');\n        break;\n}\n\n\n\nreturn div;"}}, "parts": [{"type": "gapfill", "gaps": [{"answer": "{area1_exact}", "type": "jme", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showPreview": true, "showFeedbackIcon": true, "vsetRange": [0, 1], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "answerSimplification": "fractionNumbers", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkingType": "absdiff", "vsetRangePoints": 5}, {"correctAnswerStyle": "plain", "type": "numberentry", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "minValue": "siground({area1},3)", "scripts": {}, "maxValue": "siground({area1},3)", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "marks": "2", "unitTests": [], "extendBaseMarkingAlgorithm": true, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0}], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>{plotgraph(1,0,x1,-2,ymax1,a1,0,0)}</p>\n<p>This is the graph of the function $f(x) = \\simplify[fractionNumbers]{x*e^({a1}*x)}$.</p>\n<p>Calculate the area of the shaded region.</p>\n<p>(i) Give your answer exactly, in terms of $e$. [[0]]</p>\n<p>(ii) (Calculator). Give your answer to 3 s.f. [[1]]</p>\n<p></p>", "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "marks": 0, "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}], "extensions": ["jsxgraph"], "tags": [], "statement": "<p>This is a mix of calculator and non-calculator questions.</p>", "name": "Maria's copy of Integration: Calculating the area under a curve. Needs integration by parts.", "advice": "<p>See 13.1, 13.2, 13.3 and 13.5 for background on definite integrals and areas.&nbsp; See 14.1 and 14.2 for integration by parts.</p>\n<p>Remember to do estimates to check for big mistakes.</p>", "variable_groups": [{"name": "(a)", "variables": ["x1", "a1", "ymax1", "area1_exact", "area1"]}], "preamble": {"css": "", "js": ""}, "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Function $f(x) = xe^{ax}$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.</p>"}, "ungrouped_variables": [], "variables": {"area1": {"name": "area1", "definition": "(x1/a1-1/a1^2)*e^(a1*x1)+1/a1^2", "templateType": "anything", "description": "", "group": "(a)"}, "x1": {"name": "x1", "definition": "random(2..4)", "templateType": "anything", "description": "", "group": "(a)"}, "ymax1": {"name": "ymax1", "definition": "x1*e^(a1*x1)+5", "templateType": "anything", "description": "", "group": "(a)"}, "area1_exact": {"name": "area1_exact", "definition": "expression((x1/a1-1/a1^2)+\"*e^(\"+a1*x1+\")+\"+1/a1^2)", "templateType": "anything", "description": "", "group": "(a)"}, "a1": {"name": "a1", "definition": "random([0.1,0.2,0.25,0.5])", "templateType": "anything", "description": "", "group": "(a)"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}