Chapter 4 : Integral Calculus

Introduction: Anti- derivatives if given derivative of a function we can work backwards to find the function from which it is derived

Introduction: Indefinite integral

Standard integral From the table, we can use this basic function to solve the integral of polynomial function, integral of exponential functions, integral of logarithmic functions and integral of trigonometric functions.

Properties of indefinite integrals

Properties of integral of polynomial functions

Examples:

Solution:

Solution:

Examples:

Solution:

Integral of Exponential Functions

Example:

Solution:

Solution:

Integral of Logarithmic Functions

Example:

Definite Integral

Basic properties of definite integrals

Example:

Solution:

Solution:

Integration by substitution

Function of a Linear Function of x Solution:

Application of integration Consumers surplus measures the difference between what consumers are willing to pay for a product or service and what they actually do pay. The supplier’s surplus measures the difference between the amount of money a supplier is willing to accept at a given price for a product and the amount the supplier actually does receive.

Applications of integration

Example: Solution:

Example:

Example: Find the equilibrium point for the given supply and demand function. Solution: