# Numerical Integration Class 11 Mathematics Solutions | Exercise - 20.1

## Chapter - 20.1

__Numerical Integration__

We all have to study numerical integration in class 11 mathematics. It is somehow similar to numerical computations chapter. But being similar doesn't mean we will be able to solve each and every questions given in the exercise. We all may get stuck somewhere while solving the questions.

Inorder to help you out we have brought the complete solution PDF of class 11 numerical integration chapter. We can only provide you the solutions of first exercise because we don't have the solutions of second exercise. Before we move towards the solution section, let's have a quick look at the topics we have to study in this chapter.

__Introduction__

__Introduction__

Numerical implies something that is associated with numbers; and integration is finding a sum or total value. Numerical integration thus literally means sum total in tems of numbers.

In mathematics, numerical integration is the name given to numerical computation of integral when it becomes very difficult or infeasible or impossible to find its exact value. In other words, numerical integration is concerned with the computation of an approximate value for the definite integral rather than finding an exact value. Various methods of numerical are known. We shall however be concerned with two methods, namely, the Trapezoidal Rule and Simpson's Rule.

### Definite Integral and Area Computation

The fundamental Theorem of Calculus gives us a method of computing the definite integral of a given continuous function *f* from a to b. The method is to find, by trial and error, an anti-derivative F of *f* and then to use the equation;

When the method works, it provides an exact value for the inegral. However, the method succeeds only if the anti-derivative happens to be a function that can be described in a simple way. For many integrals one cannot find a formula for the anti-derivative, and the method fails.

Such integrals can still be computed approximately using numerical intgration. A computation of this kind becomes possible once we agree that a definite integral is nothing but a limit of sum of rectangles or trapeziums constructed to cover the region bounded by the graph of the function f, two vertical lines x a and x = b and the x-axis

#### Composite Trapezoidal Rule

One way of arriving at a more accurate numerical approximation of a definite integral is to break up the given interval [a, b] into some number n of sub-intervals, imply elementary trapezoidal rule to each interval, and then add up all the results. Use of trapezium gives rise to what is known as the trapezoidal rule. Here is how trapezoidal rule goes:

### Exercise - 20.1

In this PDF, you'll only find the solution of class 11 numerical integration chapter. Though this chapter contains 2 exercises, we only have the solution of first exercise. We apologise for not being able to provide you the solutions of second exercises.

**Note**:

__Scroll the PDF to view all Solution__You are not allowed to post this PDF in any website or social platform without permission.

## How to Download Class 11 Numerical Integration Solution PDF?

We may not have internet excess 24/7. Considering this situation we have decided you to provide PDF file so that you can do your assignment even if you are offline.

If you want to download the PDF of class 11 numerical integration chapter then follow the simple steps given below.

** Step 1:** Just below the PDF you'll see a '

*Download PDF*' button. Click on it.

__ Step 2:__ After clicking the button you'll be redirected to next page or next website.

__ Step 3:__ You'll see a verification captcha. Wait few seconds and click on '

*I am not a Robot*.'

** Step 4:** Wait for 15 seconds and scroll the page till the bottom. Click on '

*Go to Link*'.

** Step 5:** You'll reach your destination and you can

*download the PDF*file.

## Usage and Distribution Guidelines

I have already mentioned before, the PDF file you download from this site is purely for personal use. You can't redistribute the PDF or use it for commercial purpose.

We haven't added any watermark to the content included in the PDF because we believe in you. We believe that you won't use this PDF for any other purpose except personal use.

I have seen many people downloading our notes and uploading them it their own site. You are strictly prohibited to do such activities. If we find any then their content will immediately be taken down. We hold all the copyright of the PDF provided in this article.

It really takes hardwork to prepare the complete solution notes. We are distributing this notes just to help students learn more. I don't want you guys to face the same problem I used to face while solving mathematics questions. So use our PDF wisely and get well prepared to solve any mathematics problems.

If you have any queries then feel free to comment down.

exercise 4.1