56 lines
1.4 KiB
Markdown
56 lines
1.4 KiB
Markdown
---
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id: act-02-integrals-and-applications-homework
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title: "Unit 02 — Integrals and Applications"
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mode: homework
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open_at: "2026-02-01T00:00:00+01:00"
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close_at: "2026-12-31T23:59:59+01:00"
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retakes_enabled: true
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max_attempts: 999
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grade_max: 100
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---
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# Unit 02 — Integrals and Applications
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## T1
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Type: essay
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Points: 25
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Prompt: Explain the difference between an antiderivative and a definite integral (interpretation).
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Refs:
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- mat-04-integrals#antiderivative
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- mat-04-integrals#definite-integral
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Rubric:
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- Correct distinction (15)
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- Meaning/interpretation is clear (10)
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## T2
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Type: essay
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Points: 25
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Prompt: Compute the definite integral from 0 to 1 of 3x^2 dx.
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Refs:
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- mat-04-integrals#basic-integration-rules
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- mat-04-integrals#definite-integral
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Rubric:
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- Correct antiderivative and evaluation (20)
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- Clear presentation (5)
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## T3
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Type: essay
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Points: 25
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Prompt: State the fundamental theorem of calculus in your own words and explain what it connects.
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Refs:
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- mat-04-integrals#fundamental-theorem-of-calculus
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Rubric:
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- Correct statement at a high level (15)
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- Explains connection between differentiation and accumulation (10)
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## T4
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Type: essay
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Points: 25
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Prompt: Optimization mini-task: For f(x)=x^2-4x+1, find the x that minimizes f(x) and the minimum value.
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Refs:
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- mat-03-derivative-applications#optimization-workflow
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- mat-02-derivatives#critical-points
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Rubric:
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- Computes derivative and critical point correctly (15)
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- Correct minimum value and interpretation (10)
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