NCERT Solutions for Maths Class 12 Exercise 7.3
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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.
NCERT Solutions for Maths Class 12 Exercise 7.3 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.
All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.
NCERT Solutions for Maths Class 12 Exercise 7.3 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.
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NCERT Solutions for Maths Class 12 Exercise 7.1
NCERT Solutions for Maths Class 12 Exercise 7.2
NCERT Solutions for Maths Class 12 Exercise 7.4
NCERT Solutions for Maths Class 12 Exercise 7.5
NCERT Solutions for Maths Class 12 Exercise 7.6
NCERT Solutions for Maths Class 12 Exercise 7.7
NCERT Solutions for Maths Class 12 Exercise 7.8
NCERT Solutions for Maths Class 12 Exercise 7.9
NCERT Solutions for Maths Class 12 Exercise 7.10
NCERT Solutions for Maths Class 12 Exercise 7.11
NCERT Solutions for Maths Class 12 Exercise 7.3
Find the
integrals of the functions in Exercises 1 to 22.
Maths Class
12 Ex 7.3 Question 1.
sin² (2x + 5)
Solution:
∫ sin² (2x + 5)
dx = ½ ∫ [1 – cos 2(2x + 5)] dx
= ½ ∫ [1 – cos (4x + 10)] dx
=
sin 3x cos 4x
Solution:
∫ sin 3x cos 4x = ½ ∫ [sin (3x + 4x) + cos (3x – 4x)] dx
= ½ ∫ [sin 7x + sin (–x)] dx
= ½ ∫ sin 7x dx – ½ ∫ sin x dx
=
cos 2x cos 4x cos 6x dx
Solution:
∫ cos 2x cos 4x
cos 6x dx
= ½ ∫ (2 cos
2x cos 4x) cos 6x dx
= ½ ∫ (cos 6x
+ cos 2x) cos 6x dx
= ¼ ∫ (2 cos2
6x + 2 cos 2x cos 6x) dx
Maths Class
12 Ex 7.3 Question 4.
sin3 (2x + 1) dx
Solution:
∫ sin3 (2x
+ 1) dx = ¼ ∫ [3 sin (2x + 1) – sin 3(2x
+ 1)] dx
Maths Class
12 Ex 7.3 Question 5.
sin3 x cos3 x
Solution:
Maths Class 12 Ex 7.3 Question 6.
sin x sin 2x sin 3x
Solution:
∫ sin x sin 2x
sin 3x dx = ½ ∫ (2 sin x sin 2x) sin
3x dx
= ½ ∫ (cos x – cos 3x) sin 3x dx
= ¼ ∫ (2
sin 3x cos x – 2 sin 3x cos 3x) dx
= ¼ ∫ (sin 4x + sin 2x – sin 6x)dx
=
sin 4x sin 8x
Solution:
∫ sin 4x sin 8x dx
= ½ ∫ 2 sin 4x sin 8x dx
= ½ ∫ (cos 4x – cos 12x) dx
=
Solution:
Solution:
sin4 x dx
Solution:
Maths Class 12 Ex 7.3 Question 11.
cos4 2x
Solution:
Maths Class 12 Ex 7.3 Question 12.
Solution:
Solution:
Solution:
tan3 2x sec 2x
Solution:
Let I = ∫ tan3 2x sec 2x = ∫ (sec2
2x – 1) sec 2x tan 2x dx
= ∫ tan2 2x sec 2x tan 2x dx
Putting sec 2x = t,
then, 2 sec 2x tan 2x dx = dt
Maths Class
12 Ex 7.3 Question 16.
tan4 x
Solution:
Let I = ∫ tan4 x
dx = ∫ tan2 x tan2 x dx
= ∫ tan2 x (sec²
x – 1) dx
= ∫ tan2 x sec² x dx –
∫ (sec² x – 1) dx
= ∫ tan2 x sec² x dx –
∫ (sec² x + ∫ 1 dx … (i)
Putting tan x =
t, then, sec² x dx = dt
From equation (i),
we get
I = ∫ t2 dt
– tan x + x + c
= t3/3 – tan x + x + c
= 1/3 tan3 x – tan x + x + c
Maths Class
12 Ex 7.3 Question 17.
Solution:
Solution:
Solution:
Solution:
sin-1 (cos x)
Solution:
Maths Class 12 Ex 7.3 Question 22.
Solution:
Maths Class
12 Ex 7.3 Question 23.
(A) tan x + cot x + c
(B) tan x + cosec x + c
(C) –tan x + cot x + c
(D) tan x + sec x + c
Solution:
Maths Class 12 Ex 7.3 Question 24.
(A) –cot (exx) + c
(B) tan (xex) + c
(C) tan (ex) + c
(D) cot (ex) + c
Solution:
NCERT Solutions for Maths Class 12 Exercise 7.1
NCERT Solutions for Maths Class 12 Exercise 7.2
NCERT Solutions for Maths Class 12 Exercise 7.4
NCERT Solutions for Maths Class 12 Exercise 7.5
NCERT Solutions for Maths Class 12 Exercise 7.6
NCERT Solutions for Maths Class 12 Exercise 7.7
NCERT Solutions for Maths Class 12 Exercise 7.8
NCERT Solutions for Maths Class 12 Exercise 7.9