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CLP-2 Integral Calculus

Appendix G Solutions to Exercises

1 Integration
1.1 Definition of the Integral
1.1.8 Exercises

1.2 Basic properties of the definite integral
1.2.3 Exercises

1.3 The Fundamental Theorem of Calculus
1.3.2 Exercises

1.4 Substitution
1.4.2 Exercises

1.5 Area between curves
1.5.2 Exercises

1.6 Volumes
1.6.2 Exercises

1.7 Integration by parts
1.7.2 Exercises

1.8 Trigonometric Integrals
1.8.4 Exercises

1.9 Trigonometric Substitution
1.9.2 Exercises

1.10 Partial Fractions
1.10.4 Exercises

1.11 Numerical Integration
1.11.6 Exercises

1.12 Improper Integrals
1.12.4 Exercises

1.13 More Integration Examples

Exercises

2 Applications of Integration
2.1 Work
2.1.2 Exercises

2.2 Averages
2.2.2 Exercises

2.3 Centre of Mass and Torque
2.3.3 Exercises

2.4 Separable Differential Equations
2.4.7 Exercises

3 Sequence and series
3.1 Sequences
3.1.2 Exercises

3.2 Series
3.2.2 Exercises

3.3 Convergence Tests
3.3.11 Exercises

3.4 Absolute and Conditional Convergence
3.4.3 Exercises

3.5 Power Series
3.5.3 Exercises

3.6 Taylor Series
3.6.8 Exercises