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

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.

3. NCERT solution PDFs also provide answers to ex 7.5 questions that will help you to cross check your answers.

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

Frequently Asked Questions

Question 1. How can I score good marks in class 12 maths chapter ex 7.5?

Answer 1. You must continue practicing if you want to do well on chapter 7 ex 7.5 of class 12 maths. You must  write all of the important highlights in the notebook provided in NCERT solutions for class 12 maths ex 7.5 at eSaral. This will assist you in remembering the concepts and topics you have studied. This will help you to better understand the concepts to score good marks in exams.

Question 2. Is ex 7.5 class 12 maths chapter available in PDF format to download?

Answer 2. Yes, ex 7.5 class 12 maths chapter 7 is available in PDF format to download from the official website of eSaral. You can easily download the PDFs online and practice the questions offline anytime.