---
id: act-02-integrals-and-applications-homework
title: "Unit 02 — Integrals and Applications"
mode: homework
open_at: "2026-02-01T00:00:00+01:00"
close_at: "2026-12-31T23:59:59+01:00"
retakes_enabled: true
max_attempts: 999
grade_max: 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)