// Numbas version: exam_results_page_options {"name": "Standard Integration", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "variables": {"a": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "name": "a"}, "m": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "name": "m"}}, "name": "Standard Integration", "advice": "

The standard rule for differentiation of polynomial expressions is

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\$f(x) = ax^n\$
\$\\frac{d(f(x))}{dx}=anx^{n-1}\$

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For this example...

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Integrate the following function $f(x)$ using the standard rule for polynomials.

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Differentiate $f(x) = ax^m$.

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The standard rule for integration of polynomial expressions is

\n

\$f(x) = ax^n\$
\$\\int f(x)\\,dx=\\frac{ax^{n+1}}{n+1}\$

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$\\displaystyle \\simplify[std]{f(x) = {a}x ^ {m} }$

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$\\displaystyle \\int f(x)\\,dx=\\;$[[0]]

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Clicking on Show steps gives you more information, you will not lose any marks by doing so.

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