Definite Integrals
Riemann sums, definite integral definition, properties, and the Fundamental Theorem of Calculus
Written and reviewed by the Study Mondo Education TeamLast updated
🎯⭐ INTERACTIVE LESSON
Try the Interactive Version!
Learn step-by-step with practice exercises built right in.
∫ Definite Integrals
Master Riemann sums, the definite integral, properties, and both parts of the Fundamental Theorem of Calculus.
Explain using:
📋 AP Calculus AB — Exam Format Guide
⏱ 3 hours 15 minutes📝 51 questions📊 4 sections
| Section | Format | Questions | Time | Weight | Calculator |
|---|---|---|---|---|---|
| Multiple Choice (No Calculator) | MCQ | 30 | 60 min | 33.3% | 🚫 |
| Multiple Choice (Calculator) | MCQ | 15 | 45 min | 16.7% | ✅ |
| Free Response (Calculator) | FRQ | 2 | 30 min | 16.7% | ✅ |
| Free Response (No Calculator) | FRQ | 4 | 60 min | 33.3% | 🚫 |
📊 Scoring: 1-5
5
Extremely Qualified
~20%
4
Well Qualified
~17%
3
Qualified
~19%
2
Possibly Qualified
~22%
1
No Recommendation
~22%
💡 Key Test-Day Tips
- ✓Show all work on FRQs
- ✓Use proper notation
- ✓Check units
- ✓Manage your time
⚠️ Common Mistakes: Definite Integrals
Avoid these 4 frequent errors
🌍 Real-World Applications: Definite Integrals
See how this math is used in the real world
📝 Worked Example: Related Rates — Expanding Circle
Problem:
A stone is dropped into a still pond, creating a circular ripple. The radius of the ripple is increasing at a rate of cm/s. How fast is the area of the circle increasing when the radius is cm?
2Write the relationship between variables
3Differentiate both sides with respect to time
4Substitute known values
🎴
Practice with Flashcards
Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.
📖
Browse All Topics
Explore more AP Calculus AB topics
📌 Related Topics in Integration
❓ Frequently Asked Questions
What is Definite Integrals?▾
Riemann sums, definite integral definition, properties, and the Fundamental Theorem of Calculus
How can I study Definite Integrals effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Definite Integrals study guide free?▾
Yes — all study notes, flashcards, and practice problems for Definite Integrals on Study Mondo are free to access. No account is needed.
What course covers Definite Integrals?▾
Definite Integrals is part of the AP Calculus AB course on Study Mondo, specifically in the Integration section. You can explore the full course for more related topics and practice resources.