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
- Moment of Inertia
- Pappus’s Theorem
- Integrals in Electric Circuits