Integration Techniques Summary
Summary of common techniques.
1. 观察法
- Inspect the structure.
- Recall known formulas.
- Try simple substitutions.
2. 分解法
- Split into simpler parts.
- Use linearity.
- Integrate term by term.
3. 变量替换法
- Choose a substitution that simplifies.
- Change limits if definite; back-substitute.
4. 恒等变换法
- Use trig/algebraic identities to simplify.
常见错误
1. 变量替换错误
Errors: forgetting to back-substitute; poor substitution choice.
Fix: always revert to original variable; pick substitutions that simplify.
2. 积分公式错误
Errors: misusing formulas; omitting .
Fix: analyze the integrand; always add .
3. 计算错误
Errors: algebra slips.
Fix: check each step carefully.
Summary
| 符号 | 类型 | 读音/说明 | 在本文中的含义 |
|---|---|---|---|
| 数学符号 | integral | 不定积分符号 |