// Numbas version: exam_results_page_options {"name": "cormac's copy of Definite Integrals 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"vsetrange": [0, 1], "checkingaccuracy": 0.001, "showCorrectAnswer": true, "checkvariablenames": false, "type": "jme", "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "scripts": {}, "vsetrangepoints": 5, "showFeedbackIcon": true, "showpreview": true, "answer": "2/pi", "prompt": "

$\\int_0^1\\cos(\\frac{\\pi t}{2})\\mathrm{dt}$.

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To write $\\pi$ in your answer simply write pi.

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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.

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Definite Integrals

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Definite Integrals

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Find the following definite integrals

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