// Numbas version: exam_results_page_options {"name": "Definite Integrals (b) (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": [], "functions": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Definite Integrals

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$\\int_0^1\\frac{e^z+1}{e^z+z}\\mathrm{dz}$.

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Express your answer using the natural log, ln().

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Hint: make a substition using the lower line.

", "customMarkingAlgorithm": "malrules:\n [\n [\"ln(1)-ln(0)\", \"You must sub back in for $u$ before filling in your limits of integration. Also, note that $\\\\ln(0)$ does not exist. $\\\\ln(x)$ is only defined for positive values of $x$. Try entering $\\\\ln(0)$ into your calculator.\"],\n [\"1/(e+1)-1\",\"You didn't actually integrate before subbing back in for $u$.\"],\n [\"1-1/0\",\"You didn't actually integrate. You simply subbed in for $e^z+z$. Also, note that $\\\\frac{1}{0}$ is not defined so that should highlight that something is wrong!\"]\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 )))Definite Integrals

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Find the following definite integral

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