# Xam Idea Class 12 Maths Chapter 8 Solutions: Integrals

Xam Idea Class 12 Maths Solutions Chapter 8 ‘Integrals’ is a must-use solution book for those who are willing to strengthen their concepts for their upcoming Class 12 board exams. Our Xam Idea solutions will explain to you everything about indefinite and definite integrals. You will be introduced to several properties, formulas, examples, applications of integrals in detail. This includes concepts like integration by parts, integrals by partial functions, area between two curves and average function.

Xam Idea solutions for Class 12 Integrals contain 100 questions built on the concepts throughout the chapter. For providing ease, the questions are settled in three sections based on the difficulty level. The simple questions are in the Very-Short type, the intermediate level questions are in the Short type whereas the advanced questions are grouped into two subsections of the Long-Answer type. You will find different kinds of questions on properties of definite integrals, substitution method, integration by part, partial fractions integration in these sections. All these questions are based on the current CBSE Class 12 exam pattern.

Instasolv’s solutions for Xam Idea Class 12 Maths Integrals can be a great assistance for preparing integrals from basics to advanced level. We provide you with comprehensive solutions that will help you become an expert on integrals. We not only provide you with solutions to Xam Idea textbook problems but also give certain tips and formula tricks so that you can manage your crucial time effectively in competitive exams. Integrals is a fundamental of calculus and is a relevant topic for board exams as well as several entrance exams like JEE Mains and Advanced. So we have plotted these solutions after advanced research of topics that are included in this chapter.

## Important Topics Of Xam Idea Class 12 Maths Solutions Chapter 8: Integrals

Since you know the importance of Integrals to score well in your exams. We here discussed some useful definitions and concepts involved in Xam Idea Class 12 Maths Solutions Chapter 8: Integrals.

**What are Integrals?**

Before, we head towards the properties and applications of Integrals. Let’s have a brief outlook of Integrals first.

Do you know the Infinitesimal data? Infinitesimal data are certain quantities in mathematics that is not actually zero, but much closer to it. So, integration here is nothing but a technique or you can say it’s an operation to put infinitesimal data into a single system. Since you know it’s fundamental in Calculus, it describes the displacement, area, volume, and several concepts that are related to Infinitesimal data. Integrals are divided into two categories-

**Definite Integrals:**

If we consider integration within boundaries, the integration used is referred to as definite integration.

Let’s say we have a closed interval [a,b].

Here, a and b are considered as boundaries in which ‘a’ is lower limit while ‘b’ is the upper limit.

Definite Integral can be defined as-

**Indefinite Integrals**

Here, boundaries have no importance in terms of finding an integration. As the name suggests, it’s a type of integration that is used to put infinitesimal data into a combined single system without restrictions. It is actually the reverse of differentiation that’s why it is termed as the antiderivative.

See here, the indefinite integrals are defined as-

In indefinite Integrals, a constant C must be introduced in the answer.

Now, see here we have listed some important formulas that are useful for solving questions involved in this chapter.

**Applications Of Integrals**

Integrals are applied for describing most of the aspects that arise from infinitesimal data. We have discussed some of them here:

- Integrals are the most commonly used technique to determine the area between two curves.
- You know the concepts of centre of mass in the physical world, integrals are also applied to find the centre of mass of a system of bodies.
- Integrals are often used to compute the average value of several functions.
- Has applications in Distance, velocity, and acceleration
- For finding a volume, integrals can be used.
- Kinetic Energy, work.
- Integrals also have its applications in determining the probability of a function.

**Integration By Parts**

Like, In Differentiation, for finding the integration of products of the functions, we have introduced Integration by parts for performing integration on functions like that.

**Integration By Partial Fractions**

For finding the Integration of rational functions, we have used Partial fractions integration. We are enlisting several forms of partial fraction integration. Have a look at them-

Apart from this, you will be introduced to some other integration types, that we will study through the questions given in exercises.

### Exercise Discussion Of Xam Idea Class 12 Maths Solutions Chapter 8: Integrals

Xam Idea Class 12 Maths Solutions for Integrals include 100 questions divided into 4 exercises as given below.

**Very Short Answer Type Questions**

- In the first section, you will be introduced to mixed questions based on indefinite integrals, definite integrals and the properties of integrals.
- There are a total of 16 questions in this exercise that have been grouped into two sections.

**Short Answer Type Questions**

- In this section, you are given 9 around problems with their solutions, which are settled in two parts.
- Part 1 has 5 odd questions in which 3 questions are from the Indefinite Integrals whereas rest 2 are from Definite integrals. The questions are generally based on the substitution method.
- While the second part consists of 4 questions in which 3 questions from the definite integral part, that uses the properties of definite integrals.
- You need to go through the properties involved in the definite integrals to tackle these kinds of questions.

**Long Answer Type Questions Type I **

- This exercise includes questions revolving around the partial fractions and Integration by type. You need to go through first, several forms of partial fraction formulas and integration by part formula as well, to cope with these questions.
- This section will provide you with a total of 56 questions carved up in two parts. In the first part, there are 48 problems that will help you anticipate the question types. All you need to do is practice these questions, as they pose a great chance to come in your exam.
- While the rest 8 problems are in the second part for practice questions. Questions are from some special types of integration.
- You will have integrals of logarithmic functions, trigonometric functions in these parts.

**Long Answer Type Questions Type II**

- This section has 19 odd problems based on the several properties of integrals involved in this chapter.
- Questions from definite integrals and partial fractions are included in this section. In one of the questions, you will be asked to evaluate the Integral as a limit of sums.

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