Applications of Integration — Class 12 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 12 Mathematics, Chapter 9. Area between curves, volumes of revolution and improper integrals.
1. About this chapter
This chapter covers Applications of Integration as part of the Class 12 Samacheer Kalvi Mathematics curriculum. It deals with area between curves, volumes of revolution and improper integrals and builds conceptual understanding essential for the TN HSC Public Exam.
By the end of this chapter, students will be able to:
- Find areas under and between curves
- Calculate volumes of revolution using disk and shell methods
2. Key concepts
- Concept 1: Find areas under and between curves.
- Concept 2: Calculate volumes of revolution using disk and shell methods.
3. Important terms and formulas
| Term / Formula | Description |
|---|---|
| Find areas under and… | Find areas under and between curves |
| Calculate volumes of revolution… | Calculate volumes of revolution using disk and shell methods |
4. Worked examples
Example 1. Applying a key concept from this chapter.
Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.
Example 2. A typical exam-style question on applications of integration.
Solution: Break the problem into steps, use the appropriate formula and verify the answer.
5. Common mistakes
- Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
- Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.
6. Practice (exam-style)
- Define the main term or principle covered in Chapter 9.
- Give two real-life examples related to applications of integration.
- Solve a short numerical or descriptive question from this chapter.
- State one important formula and explain each symbol.
7. Answer key (hints)
- Refer to section 2 (Key concepts) above for the definition.
- Examples should be drawn from daily experience and local context.
- Apply the formula from section 3, show all steps clearly.
- Formula with units — refer to the textbook glossary for symbol meanings.
8. Quick revision
- Class 12 Mathematics — Chapter 9: Applications of Integration.
- Core idea: Area between curves, volumes of revolution and improper integrals.
- Key outcomes: Find areas under and between curves; Calculate volumes of revolution using disk and shell methods.
- Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.
