// Numbas version: exam_results_page_options {"name": "Generelle integrasjonsregler ubestemte integraler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Generelle integrasjonsregler ubestemte integraler", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

Finn det ubestemte integralet for den oppgitte funksjonen.

\n

(Bruk C eller c for integrasjonskonstanten.)

", "advice": "

Bruk følgende generelle integrasjonsregler

\n

\\[ \\int a\\cdot f(x) dx =a\\cdot \\int f(x) dx \\]  ($a$ er et konstant)

\n

\\[ \\int \\big[f(x)+g(x)\\big] dx =\\int f(x) dx+\\int g(x) dx \\]

\n

\\[ \\int \\big[f(x)-g(x)\\big] dx =\\int f(x) dx-\\int g(x) dx \\]

\n

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp1": {"name": "inp1", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out1": {"name": "out1", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..33)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(5..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "inp2": {"name": "inp2", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp3": {"name": "inp3", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp4": {"name": "inp4", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp5": {"name": "inp5", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp6": {"name": "inp6", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp7": {"name": "inp7", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp8": {"name": "inp8", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out2": {"name": "out2", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out3": {"name": "out3", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out4": {"name": "out4", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out5": {"name": "out5", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out6": {"name": "out6", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

\\[ \\simplify{{out1}}(\\simplify{{inp1}})=\\simplify{{k1}*sin({k3}{inp1})-{k2}*{inp1}^{{a}}+1/{inp1}},  \\var{inp1}>0\\]

\n

\\[ \\int \\simplify{{out1}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-k1/k3}*cos({k3}*{inp1})-{k2/(a+1)}*{inp1}^({a+1})+ln({inp1})+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}]}]}], "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}]}