Brief Overview

There are 5 subtopics in this chapter:
i) Integration of functions
ii) Integration of trigonometric functions
iii) Techniques of integration
iv) Definite integrals
v) Trapezoidal rule

In integration of functions, you will learn how to integrate using basic rules of integration. Make sure to pay attention to the type of functions involve (which is: linear function). 

Next, we are going to integrate the trigonometric functions. You might need to refer to your notes from the first semester (how to use the sum to product and product to sum rule). 

However, some of functions are not really straight forward to integrate. We cannot use basic rules of integration. Hence, we need to try to use either substitution, integration by parts or by using partial fractions. If you can see the derivative of the other function, you might want to choose substitution. In integration by parts, make sure to be careful when choosing the u and dv. Normally, we will choose u that is easier to differentiate compare to integrate. Meanwhile, we only use partial fraction if we have polynomial over polynomial. By using partial fraction, we simplified the expression into something that can be solve by using basic rules of integration.

Then, we will learn how to calculate the definite integral. We will substitute the upper and the lower limit of integral. By doing so, you can calculate the area under the curve. After that, you will rotate or revolve the function to calculate the volume. 

Lastly, we will try to approximate the area for functions that are hard to integrate. We will use equal width trapezium to approximate the value. Sometimes we might need to compare the value with the exact value that we get after we integrate the function. Make sure to pay more attention to the number of intervals, width as well as the number of ordinates involved when approximating the area using trapezoidal rule.