Tutorial 1: Indefinite Integrals
Tutorial problems covering basic integration, substitution method, and integration by parts.
Sections
Basic Integration (Problems 1-4)
- Power rule applications
- Trigonometric integrals
- Exponential and logarithmic integrals
- Combining basic rules
Integration by Substitution (Problems 5-8)
- Simple substitutions ($u = ax + b$)
- Trigonometric substitutions
- Exponential substitutions
- Recognizing derivative patterns
Mixed Integration Techniques (Problems 9-12)
- Problems requiring multiple approaches
- Choosing appropriate methods
Key Techniques Practiced
- Basic antiderivatives: reversing differentiation rules
- Substitution: identifying $u$ and $du$
- Pattern recognition: spotting composite functions
- Algebraic manipulation: rewriting integrands