#### Overview of this book

Mastering SciPy
Credits
www.PacktPub.com
Preface
Free Chapter
Numerical Linear Algebra
Interpolation and Approximation
Differentiation and Integration
Nonlinear Equations and Optimization
Initial Value Problems for Ordinary Differential Equations
Computational Geometry
Descriptive Statistics
Inference and Data Analysis
Mathematical Imaging
Index

## Integration

To achieve a definite integration of functions on suitable domains, we have mainly two methods—Numerical integration and Symbolic integration.

Numerical integration refers to the approximation of a definite integral by a quadrature process. Depending on how the function f(x) is given, the domain of integration, the knowledge of its singularities, and the choice of quadrature, we have different ways to attack this problem:

• For univariate polynomials, exact integration is achieved algebraically on each finite interval

• For functions given as a finite set of samples over their domain:

• The composite trapezoidal rule

• Simpson's trapezoidal rules

• Romberg integration scheme

• For generic univariate functions given as Python functions, on finite intervals: