Integration Using Tables and Computer Algebra Systems
MAT1242: Calculus II
University of Eswatini.
Integration is a fundamental concept in calculus, allowing us to find the area under curves and solve a
wide range of problems. In this comprehensive guide, we’ll explore integration using tables and computer
algebra systems (CAS). We’ll cover the following topics:
1. Introduction to Integration
2. Using Tables for Integration
3. Leveraging Computer Algebra Systems (CAS)
4. Step-by-Step Examples
1. Introduction to Integration
Integration involves finding the antiderivative of a function. It allows us to compute the area under a
curve, evaluate definite integrals, and solve various real-world problems. There are different techniques
for integration, including substitution, integration by parts, and partial fractions.
2. Using Tables for Integration
Tables of integrals provide precomputed antiderivatives for common functions. These tables are valuable
tools for evaluating integrals quickly. Let’s look at some common integrals and their corresponding
antiderivatives:
Common Integrals and Antiderivatives
Function (f(x)) Antiderivative (F(x))
MAT1242: Calculus II
University of Eswatini.
Integration is a fundamental concept in calculus, allowing us to find the area under curves and solve a
wide range of problems. In this comprehensive guide, we’ll explore integration using tables and computer
algebra systems (CAS). We’ll cover the following topics:
1. Introduction to Integration
2. Using Tables for Integration
3. Leveraging Computer Algebra Systems (CAS)
4. Step-by-Step Examples
1. Introduction to Integration
Integration involves finding the antiderivative of a function. It allows us to compute the area under a
curve, evaluate definite integrals, and solve various real-world problems. There are different techniques
for integration, including substitution, integration by parts, and partial fractions.
2. Using Tables for Integration
Tables of integrals provide precomputed antiderivatives for common functions. These tables are valuable
tools for evaluating integrals quickly. Let’s look at some common integrals and their corresponding
antiderivatives:
Common Integrals and Antiderivatives
Function (f(x)) Antiderivative (F(x))
