RD Sharma Class 12 Exercise 18.4 Indefinite Integrals Solutions Maths

RD Sharma Class 12 Exercise 18.4 Indefinite Integrals Solutions Maths - Download PDF Free Online

Edited By Kuldeep Maurya | Updated on Jan 25, 2022 08:52 AM IST

The RD Sharma books are the most recommended solution books by most of the CBSE schools. Students find it as their excellent companions while solving sums in mathematics. However, the students face challenges when they try to develop their knowledge in chapter 18. This makes them lose interest in Indefinite Integrals. In such cases, the RD Sharma Class 12th Exercise 18.4 book plays a predominant role.

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RD Sharma Class 12 Solutions Chapter18 Indefinite Integrals - Other Exercise
Indefinite Integrals Excercise:18.4
RD Sharma Chapter wise Solutions

Also Read - RD Sharma Solutions For Class 9 to 12 Maths

RD Sharma Class 12 Solutions Chapter18 Indefinite Integrals - Other Exercise

Indefinite Integrals Excercise:18.4

Indefinite integrals exercise 18.4 question 1

Answer:
$\frac{x^{2}}{2}+3x-4\log \left | x+2 \right |+C$
Hint:
Divide numerator by denominator.
Given:
$\int \frac{x^{2}+5x+2}{x+2}$
Solution:
$\int \frac{x^{2}+5x+2}{x+2}$
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$\Rightarrow \int \left ( x+3 \right )dx-4\int \frac{1}{\left ( x+2 \right )}dx$ $\left [ \int x^{n}dx=\frac{x^{n+1}}{n+1}+C \right ]$ & $\left [ \int \frac{1}{x}dx=\log \left | x \right |+C \right ]$
$\Rightarrow \int xdx+3\int dx-4\int \frac{1}{\left ( x+2 \right )}dx$ $\Rightarrow \frac{x^{2}}{2}+3x-4\log \left | x+2 \right |+C$

Indefinite integrals exercise 18.4 question 2

Answer:
$\Rightarrow \frac{x^{3}}{3}+x^{2}+4x-8\log \left | x-2 \right |+C$
Hint:
Divide denominator by numerator.
Given:
$\Rightarrow \int \frac{x^{3}}{x-2}dx$
Solution:
$\Rightarrow \int \frac{x^{3}}{x-2}dx$
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$\Rightarrow \int \left ( x^{2}+2x+4 \right )dx+\frac{8}{\int \left ( x-2 \right )}dx$ $\left [ \int x^{n}dx=\frac{x^{n+1}}{n+1}+C \right ]$ & $\left [ \int \frac{1}{x}dx=\log \left | x \right |+C \right ]$
$\Rightarrow \int x^{2}dx+2\int xdx+4\int dx+8\int \frac{dx}{\left ( x-2 \right )}$
$\Rightarrow \frac{x^{3}}{3}+x^{2}+4x-8\log \left | x-2 \right |+C$

Indefinite integrals exercise 18.4 question 3

Answer:
$\Rightarrow \frac{x^{2}}{6}+\frac{1}{4}x^{}+\frac{43}{27}\log \left | 3x+2 \right |+C$
Hint:
Use integral by partial fraction.
Given:
$\int \frac{x^{2}+x+5}{3x+2}dx$
Solution:
$\int \frac{x^{2}+x+5}{3x+2}dx$
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So, we can write equation as
$I=\frac{1}{3}\int x dx+\frac{1}{9}\int dx+\frac{43}{9}\int\frac{1}{3x+2}dx$
$I= \frac{x^{2}}{6}+\frac{1}{9}x+\frac{43}{27}\log \log \left | 3x+2 \right |+C$

Indefinite integrals exercise 18.4 question 4

Answer:
$2\log \left | x-1 \right |-\frac{5}{x-1}+C$
Hint:
Use integration by partial fraction.
Given:
$\int \frac{2x+3}{\left ( x-1 \right )^{2}}dx$
Solution:
$\frac{2x+3}{\left ( x-1 \right )^{2}}$
$=\frac{2x-2+2+3}{\left ( x-1 \right )^{2}}$
$=\frac{2\left ( x-1 \right )+5}{\left ( x-1 \right )^{2}}$
$=\frac{2}{\left ( x-1 \right )}+\frac{5}{\left ( x-1 \right )^{2}}$
$I=\int \frac{2}{x-1}dx+\int \frac{5}{(x-1)^{2}}dx$

$\left [ \int \frac{1}{x}dx= \log \left | x \right |+C \right ]=2$
$I= \log \left | x-1 \right |-\frac{5}{x-1}+C$

Indefinite integrals exercise 18.4 question 5

Answer:
$x+\log \left | x+1 \right |+\frac{3}{x+1}+C$
Hint:
Use integration by partial fraction.
Given:
$\int \frac{x^{2}+3x-1}{\left ( x+1 \right )^{2}}dx$
Solution:
$\int \frac{x^{2}+3x-1}{\left ( x+1 \right )^{2}}dx$
$I=\int 1\cdot dx+\int \frac{x-2}{(x+1)^{2}}dx$
Put $x+1=t\Rightarrow dx=dt$
$I=x+\int \frac{t-3}{t^{2}}dt\\ \\ \Rightarrow\hspace{1cm}I=x+\int \frac{1}{t}dt-3\int \frac{1}{t^{2}}dt\\ \\ \Rightarrow\hspace{1cm}I=x+\log\left | t \right |+\frac{3}{t}+c\\ \\ \Rightarrow\hspace{1cm}I=x+\log \left | x+1 \right |+\frac{3}{x+1}+c$

Indefinite integrals exercise 18.4 question 6

Answer:
$2\log \left | x-1) \right |-\frac{1}{(x-1)}+C$
Hint:
Use integration by partial fraction.
Given:
$\int \frac{2x-1}{\left ( x-1 \right )^{2}}dx$
Solution:
$\frac{2x-1}{\left ( x-1 \right )^{2}}$
$=\frac{2(x-1)+1}{\left ( x-1 \right )^{2}}$
$=\frac{2}{x-1}+\frac{1}{(x-1)^{2}}$
$\Rightarrow \int \frac{2x-1}{\left ( x-1 \right )^{2}}dx=\int \left [ \frac{2}{x-1} +\frac{1}{(x-1)^{2}}\right ]dx$
$=2\int \frac{1}{x+1}dx+\int \frac{1}{(x-1)^{2}}dx$
$=2\log \left | x-1) \right |-\frac{1}{(x-1)}+C$

RD Sharma Class 12 Solutions Indefinite Integrals Ex 18.4 is one of the most challenging portions present in the syllabus. This chapter consists of 32 exercises, ex 18.1 to ex 18.32. The first few exercises deal with the basic integration sums. The fourth exercise, ex 18.4, contains six questions to be solved. The central concept in this exercise is evaluating the integrals in the given form. If you have doubts about solving these sums, use the RD Sharma Class 12 Chapter 18 Exercise 18.4 solution book.

This portion must be clear as the sums get a bit harder in the following exercises. Hence, understanding the foundation in Indefinite Integrals is very important to have a strong foundation in the concept. The RD Sharma Class 12th Exercise 18.4 follows the NCERT syllabus. This makes the students of CBSE adapt to it easily. The students can complete their homework, do their assignments and even prepare for the exam.

If you struggle to understand the concepts in chapter 18, get the help of the Class 12 RD Sharma Chapter 18 Exercise 18.4 Solution material to understand the concept and steps easily. Integrations will be no harder if you do regular practice in it until you are well versed. If there is any other easy way to solve the sums, it is also given in the RD Sharma books. In such instances, you will have the choice to select the method you would like to adopt.

Looking at the benefits, you attain using the RD Sharma Class 12 Solutions Indefinite Integrals, you need not think that it would cost a lot. RD Sharma Class 12 Solutions Chapter 18 ex 18.4 solution books are now available for free download from the Career360 website. Hence, without even paying a single rupee, you can utilize the benefits of the best set of solution books.

As the RD Sharma Class 12th Exercise 18.4 books are widely used by many students and teachers, there is a lot of chance that the questions for the public exam would be picked from this book. Hence practicing with the RD Sharma Class 12 Solutions Chapter, 18 Ex 18.4 will help you score high marks in the exams.

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Frequently Asked Questions (FAQs)

1. How many questions are there in Class 12 RD Sharma chapter 18?

There are a total of 14 questions in RD Sharma Solutions Class 12 RD Sharma chapter 18 exercise 18.32.

2. How many exercises are there in Chapter 18?

There are a total of 32 exercises, i.e., from 18.1 to 18.32.

3. How can I access the solution of RD Sharma chapter 18 exercise 18.30 for class 12?

Class 12 RD Sharma Chapter 18 Exercise 18.30 Solution is available on Career360's website and is free to access.

4. Do RD Sharma Relations Ex 18.30 class 12 solutions follow the latest version of the book?

Yes, the Class 12 RD Sharma Chapter 18 Exercise 18.4 Solution is updated to the latest version.

5. What are the benefits of this material?

This material is the best alternative for students who want to get more knowledge and score better marks in exams. It contains solved questions prepared by experts that help students perform well in exams.