This material gives a straightforward introduction to techniques of integration, which is one of the most difficult areas of calculus. A lot of completely worked examples are used to introduce methods of integration and to demonstrate problem-solving techniques. The topics are written as self-guided tutorials. Each page contains necessary definitions and formulas, which are illustrated by typical problems with detailed solutions.

• Antiderivatives and Initial Value Problems
• The Indefinite Integral and Basic Rules of Integration. Table of Integrals
• Integration by Substitution
• Integration by Parts
• Integration by Completing the Square
• Partial Fraction Decomposition
• Integration of Rational Functions
• Integration of Irrational Functions
• Weierstrass Substitution
• Trigonometric Integrals
• Integration of Hyperbolic Functions
• Integrals of Vector-Valued Functions
• Trigonometric and Hyperbolic Substitutions
• Riemann Sums and the Definite Integral
• The Fundamental Theorem of Calculus
• Trapezoidal Rule
• Simpson’s Rule
• Improper Integrals
• Area of a Region Bounded by Curves
• Volume of a Solid with a Known Cross Section
• Volume of a Solid of Revolution: Disks and Washers
• Volume of a Solid of Revolution: Cylindrical Shells
• Area of a Surface of Revolution
• Average Value of a Function
• Probability Density Function
• Arc Length
• The Net Change Theorem
• Distance, Velocity and Acceleration
• Force, Work and Energy
• Mass and Density
• Center of Mass and Moments