Visions of Mathematics: Integrals

1. Indefinite Integral

2. Integrals of Rational Functions

3. Integrals of Irrational Functions

4. Integrals of Trignometric Functions

5. Integrals of Hyperbolic Functions

6. Integrals of Exponentional and Logarithmic Functions

7. Reduction Formulas

8. Definite Integral

9. Improper Integral

The definite integral $\int_{a}^{b} f(x) \: \: dx$ is called an improper integral if

a or b is infinite
f(x) has one or more points of discontinuity in the interval [a,b]

If f(x) is a continuous function on [a, $\infty$ ), then

$\int_{a}^{b} f(x) \: \: dx = lim \: n \to \infty \: \int_{a}^{\infty} f(x) \: \: dx$

10. Double Integral

11. Triple Integral

12. Line Integral

Line integral of a Scalar Function

13. Surface Integral

14. Numerical Integration

The trapezium rule