Calculus 2
Master integration techniques, sequences, series, and convergence tests.
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∫ Integration Techniques
Integration is the reverse process of differentiation. Learn various techniques to solve complex integrals.
Key Methods:
- • U-Substitution
- • Integration by Parts
- • Trigonometric Substitution
- • Partial Fractions
- • Improper Integrals
📊 Applications of Integrals
Integrals have powerful applications in calculating areas, volumes, and other physical quantities.
Applications:
- • Area between curves
- • Volumes of solids of revolution
- • Arc length of curves
- • Surface area of revolution
- • Work and fluid pressure
∞ Sequences and Series
Sequences and series help us understand infinite sums and their convergence properties.
Convergence Tests:
- • Ratio Test
- • Root Test
- • Integral Test
- • Comparison Tests
- • Alternating Series Test
- • P-Series Test
📈 Taylor and Maclaurin Series
Taylor series represent functions as infinite polynomial sums, providing powerful approximation tools.
Key Concepts:
- • Taylor polynomial approximations
- • Maclaurin series (Taylor series at x=0)
- • Radius and interval of convergence
- • Common series expansions (e^x, sin(x), cos(x))
Practice your series calculations with our calculators and track your progress with FlashForge (cardsmith.io) flashcards.
🎓 Ready to Practice?
Use our interactive calculators to master integration and series.