calculus/activities/02-integrals-and-applications-homework.md
2026-01-01 00:00:00 +00:00

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act-02-integrals-and-applications-homework Unit 02 — Integrals and Applications homework 2026-02-01T00:00:00+01:00 2026-12-31T23:59:59+01:00 true 999 100

Unit 02 — Integrals and Applications

T1

Type: essay Points: 25 Prompt: Explain the difference between an antiderivative and a definite integral (interpretation). Refs:

  • mat-04-integrals#antiderivative
  • mat-04-integrals#definite-integral Rubric:
  • Correct distinction (15)
  • Meaning/interpretation is clear (10)

T2

Type: essay Points: 25 Prompt: Compute the definite integral from 0 to 1 of 3x^2 dx. Refs:

  • mat-04-integrals#basic-integration-rules
  • mat-04-integrals#definite-integral Rubric:
  • Correct antiderivative and evaluation (20)
  • Clear presentation (5)

T3

Type: essay Points: 25 Prompt: State the fundamental theorem of calculus in your own words and explain what it connects. Refs:

  • mat-04-integrals#fundamental-theorem-of-calculus Rubric:
  • Correct statement at a high level (15)
  • Explains connection between differentiation and accumulation (10)

T4

Type: essay Points: 25 Prompt: Optimization mini-task: For f(x)=x^2-4x+1, find the x that minimizes f(x) and the minimum value. Refs:

  • mat-03-derivative-applications#optimization-workflow
  • mat-02-derivatives#critical-points Rubric:
  • Computes derivative and critical point correctly (15)
  • Correct minimum value and interpretation (10)