We can solve definite integration numerically by Trapezoidal rule, Simpson’s one-third rule, and Simpson’s three-eighth rule. We will discuss each method one by one with the help of a series of video lectures. Each video tutorial contains at least one example for better understanding of the topic.
We have already discussed the solution of the system of linear equations, numerical solution of algebraic non-linear equations, and the numerical solution of differential equations in our previous posts. If you want to learn these concepts then click on their respective links.
The value of the definite integral is equal to the total area under the curve between the given limits. In Trapezoidal rule, we consider the curve as a straight line between two intervals and then we find the total area under the curve by finding the area of the trapeziums of each interval. Adding all the areas will give the total area and hence, the total area under the curve is known. Watch the video tutorial to learn this topic.
Simpson’s One-Third Rule
In Simpson’s one third rule we consider the curve as parabola or polynomial of second order and then find the area under the curve. Here we find two area at a time and summation of all areas gives the total area under the curve. And the total area under the curve is equal to the definite integral between the given limits. Learn this concept through video tutorial given below. We have included the example in the video to make the topic more clear.
Simpson’s Three-Eighth Rule
In Simpson’s Three-Eighth rule, we consider the curve as cubic equation or polynomial of third order and then we find the area of the three intervals simultaneously. After adding each area, we can find the total area. We have explained this concept with the help of one example in the video lecture given below. Watch it to grab the topic throughly.
That is all for this post. These video lectures are part of our higher engineering maths course. We have also posted the basic mathematics videos, you can have look at those courses. Keep commenting and keep motivating us through your positive feedbacks. You can also ask your doubts and queries through the comment section or by contacting us. We are always ready to help you.