NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 7.2.
Krati Saraswat3 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 Integrals is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of chapter-7. Given below is step by step solutions of all questions given in the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2.NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 Overview
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 addresses these significant subjects. In order to fully comprehend the concepts presented in the chapter and make effective use of the provided solutions, it is recommended that students go over each topic in great detail. The intention is for students to effortlessly achieve excellent exam scores after reviewing and practicing these responses.NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 Integrate the functions in Exercise 1 to 8. Question 1.
Solution :
Let 1 + x
2
=
t
∴2
x dx
=
dt
Question 2.
Solution :
Let log |
x
| =
t
∴ 1/x dx = dt
Question 3.
Solution :
Question 4.
sin
x
⋅ sin (cos
x
)
Solution :
sin
x
⋅ sin (cos
x
)
Let cos
x
=
t
∴ −sin
x dx = dt
Question 5. sin(ax + b) cos(ax + b)
Solution :
Questionc 6.
√ax + b
Solution :
Let
ax + b = t
⇒
adx = dt
Question 7.
x√x + 2
Solution :
Let (x + 2) = t
∴
dx = dt
Question 8.
x√1 + 2
x
2
Solution :
Let 1 + 2
x
2
=
t
∴ 4
xdx = dt
Integrate the functions in Exercise 9 to 17.
Question 9.
Solution :
Question 10.
Solution :
Question 11.
Solution :
Question 12.
Solution :
Let x
3
- 1 = t
∴ 3x
2
dx = dt
Question 13.
Solution :
Let 2 + 3x
3
= t
∴ 9
x
2
dx = dt
Question 14.
Solution :
Let log
x = t
∴ 1/x dx = dt
Question 15.
x/9 - 4x
2
Solution :
Let 9 - 4x
2
= t
∴ −8
x dx
=
dt
Question 16.
Solution :
Let 2x + 3 = t
∴ 2
dx = dt
Question 17.
Solution :
Let x
2
= t
∴ 2
xdx = dt
Integrate the functions in Exercise 18 to 26.
Question 18.
Solution :
Question 19.
Solution :
Dividing numerator and denominator by
e
x
, we obtain
Question 20.
Solution :
Question 21.
tan
2
(2x - 3)
Solution :
Question 22. sec
2
(7 - 4x)
Solution :
Let 7 − 4
x
=
t
∴ −4
dx = dt
Question 23.
Solution :
Question 24.
Solution :
Question 25.
Solution :
Question 26.
Solution :
Let √x = t
Integrate the functions in Exercise 27 to 37.
Question 27.
Solution :
Let sin 2
x
=
t
Question 28.
Solution :
Let 1 + sin x = t
∴ cos
x dx
=
dt
Question 29. cot
x
log sin
x
Solution :
Let log sin
x
=
t
Question 30.
sin x/1 + cos
x
Solution :
Let 1 + cos
x = t
∴ −sin
x dx
=
dt
Question 31.
sin x/(1 + cos
x)
2
Solution :
Let 1 + cos
x
=
t
∴ −sin
x
dx = dt
Question 32. 1/1 + cot x
Solution :
Question 33. 1/1 - tan x
Solution :
Question 34.
Solution :
Question 35.
Solution :
Let 1 + log
x
=
t
∴ 1/x dx = dt
Question 36.
Solution :
Question 37.
Solution :
Let
x
4
=
t
∴ 4
x
3
dx = dt
Choose the correct answer in Exercise 38 and 39.
Question 38.
equals
(A) 10
x
- x
10
+ C
(B) 10
x
+ x
10
+ C
(C) (10
x
- x
10
)
-1
+ C
(D) log(10
x
+ x
10
) + C
Solution :
Therefore, option (D) is correct.
Question 39.
equals
(A) tan x + cot x + C
(B) tan x – cot x + C
(C) tan x cot x + C
(D) tan x – cot 2x + C
Solution :
Therefore, option (B) is correct.
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 FAQs
How many exercises are there in integrals?
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 the definite integral in math class 12?
The definite integral of any function can be expressed either as the limit of a sum or if there exists an antiderivative F for the interval [a, b], then the definite integral of the function is the difference of the values at points a and b.
What are the two types of integrals?
The two types of integrals are definite integral (also called Riemann integral) and indefinite integral (sometimes called an antiderivative).
What unit is definite integral?
In general, the units for the definite integral b∫af(x)dx are (y-units )⋅(x-units). A quick check of the units can help avoid errors in setting up an applied problem.
What is the limit of integration?
Limits of integration are the upper and the lower limits, which are applied to integrals. The integration of a function ∫f(x) ∫ f ( x ) gives its antiderivative F(x), and the limits of integration [a, b] are applied to F(x), to obtain F(a) - F(b).
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