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# NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.5 Integrals - PDF Download

NCERT solutions for class 12 math chapter 7 exercise 7.5 Integrals teaches students how to find integrals using partial fractions. One simple method for decomposing and integrating a rational function with a complex polynomial function in the denominator is integration by partial fractions. Class 12 maths chapter 7 exercise 7.5 NCERT solutions has questions with answers to help you revise the concepts for preparing exams.

Ex 7.5 class 12 maths chapter 7 has a total of 23 questions in which 21 questions are short answer type and remaining 2 questions are multiple type questions. It is essential to comprehend the steps used in the partial decomposition process in order to answer these questions. These questions are solved in a simple and stepwise manner by the academic team of mathematics at eSaral to help you score good marks in exams.

Ex 7.5 class 12 maths solutions are also available in PDF format. You can easily download these solution PDFs for free from the website of eSaral and practice all the questions of ex 7.5 class 12 maths.

## Topics Covered in Exercise 7.5 Class 12 Mathematics Questions

This exercise is based on finding solutions of integration by partial fractions. This topic is described by subject experts of eSaral.

 1 Integration by Partial Fractions
1.  Integration by Partial Fractions

The ratio of two polynomials with the following form P(x)Q(x) is called a rational function, where P(x) and Q(x) are polynomials in x and Q(x) ≠ 0. The rational function is referred to as proper if the degree of P(x) is less than the degree of Q(x) otherwise, it is referred to as improper. The improper rational functions can be reduced to the proper rational functions by a long division process. Thus, if P(x)Q(x) is improper, then P(x)Q(x) = T(x) + P1(x)Q(x), where T(x) is a polynomial in x and P1(x)Q(x)is a proper rational function.

The integration of any rational function is reduced to the integration of a proper rational function. The rational functions which you shall consider here for integration purposes will be those whose denominators can be factorised into linear and quadratic factors.

Suppose we have to evaluate $\int \frac{\mathrm{P}(x)}{\mathrm{Q}(x)} d x$ , where P(x)Q(x) is a proper rational function. By using a method known as partial fraction decomposition, the integrand may always be expressed as the sum of simpler rational functions. After that, with the method learned before, integration can be completed with ease.

## Tips for Solving Exercise 7.5 Class 12 Chapter 7 Integrals

One of the primary methods used to find integrals for complex function values is the integration by partial fractions method. Here, we have provided some useful tips for solving ex 7.5 class 12 maths.

1. Students must practice the questions related to integration by partial fractions provided in NCERT solutions class 12 maths chapter 7 ex 7.5 so that they can get in-depth knowledge of the topic.

2. Students should also practice the examples based on the concepts provided in exercise 7.5.

3. Before solving exercise questions, you must be well versed with the concepts, terms and formulas used in questions of ex 7.5 for better understanding of questions.

## Importance of Solving Ex 7.5 Class 12 Maths Chapter 7 Integrals

eSaral’s subject experts have provided some important benefits of solving ex 7.5 class 12 maths chapter 7 Integrals.

1. Questions in class 12 maths chapter 7 exercise 7.5 NCERT solutions range in difficulty from moderate to advanced. Our subject experts have solved each question of ex 7.5 with a simple and step by step manner that will help you solve even difficult questions with ease.

2. Students must practice from NCERT solutions class 12 maths chapter 7 exercise 7.5 to get the deep knowledge of concepts.

4. By practicing questions in ex 7.5 class 12 maths NCERT solutions will improve your self-confidence and problem solving skills.