# Antiderivatives Class 11 Mathematics Solutions | Exercise - 18.4

## Chapter - 18  Antiderivatives

Students in class 11 learn about antiderivatives, a type of calculus in which they learn how to find the area under the curve of a function and evaluate indefinite integrals, as well as solving differential equations. Antiderivatives can be calculated using integration by substitution, integration by parts, and trigonometric substitution, all of which are methods that students learn to use in order to calculate them.

As part of the course, students learn how to use the Fundamental Theorem of Calculus to calculate antiderivatives. Moreover, they learn how to identify a function's antiderivative as well as how to use the substitution rule for integrals in order to evaluate definite integrals.

The following sections provide a brief introduction to antiderivaties and some of the subtopics related to antiderivaties as well as some basic formulas related to antiderivatives before going into the solution section.

### Introduction

Antiderivatives, also known as indefinite integrals, are the inverse operation of derivatives. In other words, an antiderivative is the original function from which a derivative was derived.

For example, the derivative of f(x) = x² is f'(x) = 2x. Therefore, the antiderivative of 2x is f(x) = x². Antiderivatives can be used to find the area under a curve, and can also be used to solve differential equations.

### Integration by Parts

If a given function to be integrated is in the product form and it cannot be integrated either by reducing the integrand into the standard form or by substitution, we use the following rule known as the integration by parts.

This formula can be stated as follows:
The integral of the product of two functions = First function Integral of second
-Integral of (Derivative of first x Integral of second)

This is the formula of the integration of the product of two functions and is known as the "Integration by parts". The successfulness of the use of the above formula depends upon the proper choice of the first function. The first function must be chosen such that its derivative reduces to a simple form and second function should be easily integrable.

### Exercise - 18.4

This PDF contains all handwritten notes of class 11 Antiderivatives chapter, including solutions of Exercise 18.4. If you want the solutions of other exercises, click the button above.

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## Is Class 11 Mathematics Guide Helpful For Student ?

I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for completing all the exercises. If you totally depend on this note and simply copy as it is then it may affect your study.

Student should also use their own will power and try to solve problems themselves. You can use this mathematics guide PDF as a reference. You should check all the answers before copying because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

## How to secure good marks in Mathematics ?

As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions .

If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.

Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied.

When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.

If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination.

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