NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.3 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.3.
- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.2
- Integrals Class 12 Ex 7.4
- Integrals Class 12 Ex 7.5
- Integrals Class 12 Ex 7.6
- Integrals Class 12 Ex 7.7
- Integrals Class 12 Ex 7.8
- Integrals Class 12 Ex 7.9
- Integrals Class 12 Ex 7.10
- Integrals Class 12 Ex 7.11
Board | CBSE |
Textbook | NCERT |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 7 |
Chapter Name | Integrals |
Exercise | Ex 7.3 |
Number of Questions Solved | 24 |
Category | NCERT Solutions |
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.3
Find the integrals of the functions in Exercises 1 to 22.
Ex 7.3 Class 12 Maths Question 1.
sin²(2x+5)
Solution:
∫sin²(2x+5)dx
= ∫[1-cos2(2x+5)]dx
= ∫[1-cos(4x+10)]dx
=
Ex 7.3 Class 12 Maths Question 2.
sin3x cos4x
Solution:
∫sin3x cos4x
= ∫[sin(3x+4x)+cos(3x-4x)]dx
= ∫[sin7x+sin(-x)]dx
=
Ex 7.3 Class 12 Maths Question 3.
∫cos2x cos4x cos6x dx
Solution:
∫cos2x cos4x cos6x dx
= ∫(cos6x+cos2x) cos6x dx
Ex 7.3 Class 12 Maths Question 4.
∫sin3(2x+1)dx
Solution:
= ∫[3sin(2x+1)-sin3(2x+1)]dx
=
=
Ex 7.3 Class 12 Maths Question 5.
sin3x cos3x
Solution:
put sin x = t
⇒ cos x dx = dt
Ex 7.3 Class 12 Maths Question 6.
sinx sin2x sin3x
Solution:
∫sinx sin2x sin3x dx
= ∫ 2sin x sin 2x sin 3x dx
= ∫ (cosx – cos3x)sin 3x dx
= ∫ (sin 4x + sin 2x – sin 6x)dx
=
Ex 7.3 Class 12 Maths Question 7.
sin 4x sin 8x
Solution:
∫sin 4x sin 8xdx
= ∫(cos 4x – cos 12x)dx
=
Ex 7.3 Class 12 Maths Question 8.
Solution:
Ex 7.3 Class 12 Maths Question 9.
Solution:
Ex 7.3 Class 12 Maths Question 10.
∫sinx4 dx
Solution:
Ex 7.3 Class 12 Maths Question 11.
cos4 2x
Solution:
∫ cos4 2x dx
Ex 7.3 Class 12 Maths Question 12.
Solution:
Ex 7.3 Class 12 Maths Question 13.
Solution:
let I =
= 2∫cos x dx + 2cos α∫dx
= 2(sinx+xcosα)+c
Ex 7.3 Class 12 Maths Question 14.
Solution:
let I =
put cosx+sinx = t
⇒ (-sinx+cosx)dx = dt
Ex 7.3 Class 12 Maths Question 15.
Solution:
I = ∫(sec22x-1)sec2x tan 2xdx
put sec2x=t,2 sec2x tan2x dx=dt
Ex 7.3 Class 12 Maths Question 16.
tan4x
Solution:
let I = ∫tan4 dx
= ∫(sec²x-1)²dx
Ex 7.3 Class 12 Maths Question 17.
Solution:
= secx-cosecx+c
Ex 7.3 Class 12 Maths Question 18.
Solution:
Ex 7.3 Class 12 Maths Question 19.
Solution:
put tanx = t
so that sec²x dx = dt
Ex 7.3 Class 12 Maths Question 20.
Solution:
put cosx+sinx=t
⇒(-sinx+cox)dx = dt
Ex 7.3 Class 12 Maths Question 21.
sin-1 (cos x)
Solution:
Ex 7.3 Class 12 Maths Question 22.
Solution:
Ex 7.3 Class 12 Maths Question 23.
(a) tanx+cotx+c
(b) tanx+cosecx+c
(c) -tanx+cotx+c
(d) tanx+secx+c
Solution:
(a)
= ∫(sec²x-cosec²x)dx
= tanx+cotx+c
Ex 7.3 Class 12 Maths Question 24.
(a) -cot(e.xx)+c
(b) tan(xex)+c
(c) tan(ex)+c
(d) cot ex+c
Solution:
(b)
= ∫sec²t dt
= tan t+c = tan(xex)+c
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