Simple Indefinite Integrals

\n", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "ungrouped_variables": ["a", "c", "b", "d", "f"], "preamble": {"css": "", "js": ""}, "rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "malrules:\n [\n [\"3/4p-p^2-4/p\",\"Don't forget the integration constant!\"],\n [\"3/4p-p^2+4ln(p^2)+C\", \"Check the third term again. $\\\\int \\\\frac{1}{p} \\\\ dp = \\\\ln p$ but $\\\\int \\\\frac{1}{p^n} \\\\ dp$ for $n \\\\neq 1$ is not $\\\\ln(p^n)$. That is, if the power on $p$ under the line is anything other than $1$, the integral is not $\\\\ln$.\"],\n [\"3/4p-p^2+4ln(p^2)\", \"Check the third term again. $\\\\int \\\\frac{1}{p} \\\\ dp = \\\\ln p$ but $\\\\int \\\\frac{1}{p^n} \\\\ dp$ for $n \\\\neq 1$ is not $\\\\ln(p^n)$. That is, if the power on $p$ under the line is anything other than $1$, the integral is not $\\\\ln$.\"],\n [\"-p^2-4/p+C\",\"It looks like you have differentiated the first term rather than integrating.\"],\n [\"-p^2-4/p\",\"It looks like you have differentiated the first term rather than integrating.\"],\n [\"-p^2+4ln(p^2)+C\",\"There are two errors here. Firstly, it looks like you have differentiated the first term rather than integrating. Secondly, $\\\\int \\\\frac{1}{p} \\\\ dp = \\\\ln p$ but $\\\\int \\\\frac{1}{p^n} \\\\ dp$ for $n \\\\neq 1$ is not $\\\\ln(p^n)$. That is, if the power on $p$ under the line is anything other than $1$, the integral is not $\\\\ln$.\"],\n [\"-p^2+4ln(p^2)\",\"There are two errors here. Firstly, it looks like you have differentiated the first term rather than integrating. Secondly, $\\\\int \\\\frac{1}{p} \\\\ dp = \\\\ln p$ but $\\\\int \\\\frac{1}{p^n} \\\\ dp$ for $n \\\\neq 1$ is not $\\\\ln(p^n)$. That is, if the power on $p$ under the line is anything other than $1$, the integral is not $\\\\ln$.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))Indefinite Integrals

", "name": "Indefinite Integrals Q7 2019 (custom feedback)", "variable_groups": [], "tags": [], "functions": {}, "statement": "Solve the following indefinite integrals, using $C$ to represent an unknown constant.

", "variables": {"f": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..8 except d)", "name": "f"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9 except a)", "name": "b"}, "c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..9 except a except b)", "name": "c"}, "a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "a"}, "d": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..8)", "name": "d"}}, "type": "question", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}