// Numbas version: exam_results_page_options {"name": "Integration: Calculating the area under a curve. Needs integration by parts.", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Integration: Calculating the area under a curve. Needs integration by parts.", "tags": [], "metadata": {"description": "

Function \$f(x) = xe^{ax}\$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.

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This is a mix of calculator and non-calculator questions.

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See 14.1, 14.2, 14.3 and 14.5 for background on definite integrals and areas.  See 15.1 and 15.2 for integration by parts.

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Remember to do estimates to check for big mistakes.

{plotgraph(1,0,x1,-2,ymax1,a1,0,0)}

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This is the graph of the function \$f(x) = \\simplify[fractionNumbers]{x*e^({a1}*x)}\$.

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Calculate the area of the shaded region.

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