NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 (Integrals)
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6: Academic team of PW uploaded errorless NCERT Solutions for Class 12 Maths Chapter-7-Integrals Exercise 7.6 prepared based on recommendations of CBSE
Krati Saraswat7 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 (Integrals)
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 Integrals is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 7. Given below is a step by step solutions to all questions given in the k for NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 .NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 Overview
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam results.NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 Integrate the functions in Exercises 1 to 8. Question 1. x sin x Solution : Let I = ∫ x sin x dx Taking x as first function and sin x as second function and integrating by parts, we obtain
Question 2.
x
sin 3
x
Solution :
Let I = ∫
x
sin
3x dx
Taking
x
as first function and sin 3
x
as second function and integrating by parts, we obtain
Question 3.
x
2
e
x
Solution :
Let I = ∫
x
2
e
x
dx
Taking
x
2
as first function and
e
x
as second function and integrating by parts, we obtain
Again integrating by parts, we obtain
Question 4.
x
log
x
Solution :
Let I = ∫
x
log
x dx
Taking log
x
as first function and
x
as second function and integrating by parts, we obtain
Question 5.
x
log 2
x
Question 6.
x
2
log
x
Solution :
Let I = ∫ x
2
log x dx
Taking log x as first function and x
2
as second function and integrating by parts, we obtain
Question 7.
x sin
-1
x
Solution :
Let I = ∫ x sin
-1
x
Taking
sin
-1
x
as first function and
x
as second function and integrating by parts, we obtain
Question 8.
x tan
-1
x
Solution :
Let I = ∫ x tan
-1
x
Taking tan
-1
x as first function and
x
as second function and integrating by parts, we obtain
Integrate the functions in Exercises 9 to 15. Question 9. x cos -1 x Solution : Let I = ∫ x cos -1 x
Taking cos −1 x as first function and x as second function and integrating by parts, we obtain
Question 10.
Solution :
Let I =
∫
.
1 dx
Taking
as first function and 1 as second function and integrating by parts, we obtain
Question 11.
Solution :
Let
Taking cos
−1
x
as first function and
as second function and integrating by parts, we obtain
Question 12.
x sec
2
x
Solution :
Let I = ∫ x sec
2
x dx
Taking
x
as first function and sec
2
x
as second function and integrating by parts, we obtain
Question 13.
tan
-1
x
Solution :
Let I = ∫
tan
-1
x dx
Taking tan
-1
x as first function and 1 as second function and integrating by parts, we obtain
Question 14.
x (log x)
2
Solution :
Let I = ∫ x (log x)
2
dx
Taking (log x)
2
as first function and
x
as second function and integrating by parts, we obtain
Question 15. (x
2
+ 1) log x
Solution :
Integrate the functions in Exercises 16 to 22.
Question 16.
Solution :
Question 17.
Solution :
Question 18.
Solution :
Question 19.
Solution :
Question 20.
Solution :
Question 21. e
2x
sin x
Solution :
Let I = ∫ e
2x
sin x
Integrating by parts, we obtain
Question 22.
Solution :
Choose the correct answer in Exercise 23 and 24.
Question 23.
equals to
Solution :
Let I =
Therefore, option (A) is correct.
Question 24.
∫
equals:
(A) e
x
cos x + C
(B) e
x
sec x + C
(C) e
x
sin x + C
(D) e
x
tan x + C
Solution :
Therefore, option (B) is correct.
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 FAQs
How many exercises are there in Chapter 7 Class 12?
NCERT Solutions for class 12 Maths Chapter 7 Integrals in Hindi and English Medium updated for CBSE session 2023-24. As per the rationalised syllabus and latest NCERT book for CBSE 2023-24, there are only 11 exercises (including miscellaneous) in chapter 7.
What is integral class 12?
Integration is the inverse process of differentiation. Instead of differentiating a function, we are given the derivative of a function and asked to find its primitive, i.e., the original. function. Such a process is called integration or anti differentiation.
Why is integration used?
Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.
Why is it called integral math?
An integral is a mathematical instance of integration in this sense. The usual meaning of integral in non-mathematical contexts is that an integral is a whole.
Who invented integration?
Greek mathematics, the principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz
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