Get Free NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.6 PDF. Integration Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 7.6 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 7 Maths Class 12 Integrals Exercise 7.6 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 Integrals PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

The topics and sub-topics included in the Integrals chapter are the following:

Section Name Topic Name
7 Integrals
7.1 Introduction
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals

NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.6

NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.6 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Integrals Ex 7.6

Integrate the functions in Exercises 1 to 22.
Question 1.
x sinx
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 1
Question 2.
x sin3x
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 2
Question 3.
\({ x }^{ 2 }{ e }^{ x }\)
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 3
Question 4.
x logx
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 4
Question 5.
x log2x
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 5
Question 6.
\({ x }^{ 2 }logx\)
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 6
Question 7.
\(x\quad { sin }^{ -1 }x\)
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 7
Question 8.
\(x\quad { tan }^{ -1 }x\)
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 8
Question 9.
\(x\quad { cos }^{ -1 }x\)
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 9
Class 12 Maths NCERT Solution Ex 7.6 Q 9 - i
Question 10.
\({ (sin }^{ -1 }{ x })^{ 2 }\)
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 10
Question 11.
\(\frac { x\quad { cos }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } } \)
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 11
Question 12.
x sec²x
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 12
Question 13.
\({ ta }n^{ -1 }x\)
Solution:
Class 12 Maths NCERT Solution Q 13
Question 14.
x(logx)²
Solution:
Class 12 Maths NCERT Solution Q 14
Question 15.
(x²+1)logx
Solution:
Class 12 Maths NCERT Solution Q 15
Class 12 Maths NCERT Solution Q 15 - i
Question 16.
\({ e }^{ x }(sinx+cosx)\)
Solution:
Class 12 Maths NCERT Solution Q 16
Question 17.
\(\frac { { xe }^{ x } }{ { (1+x) }^{ 2 } } \)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 17
Question 18.
\(\frac { { e }^{ x }(1+sinx) }{ 1+cosx } \)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 18
Ch 7 Maths Class 12 Ex 7.6 Q 18 - i
Question 19.
\({ e }^{ x }\left( \frac { 1 }{ x } -\frac { 1 }{ { x }^{ 2 } } \right) \)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 19
Question 20.
\(\frac { { (x-2)e }^{ x } }{ { (x-1) }^{ 3 } } \)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 20
Question 21.
\({ e }^{ 2x }sinx\)
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 21
Question 22.
\({ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right) \)
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 22

Choose the correct answer in exercise 23 and 24

Question 23.
\(\int { { x }^{ 2 }{ e }^{ { x }^{ 3 } } } dx\quad equals\)
(a) \(\frac { 1 }{ 3 } { e }^{ { x }^{ 3 } }+c\)
(b) \(\frac { 1 }{ 3 } +{ e }^{ { x }^{ 2 } }+c\)
(c) \(\frac { 1 }{ 2 } { e }^{ { x }^{ 3 } }+c\)
(d) \(\frac { 1 }{ 2 } { e }^{ { x }^{ 2 } }+c\)
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 23
Question 24.
\(\int { { e }^{ x }secx(1+tanx) } dx\quad equals\)
(a) \({ e }^{ x }cosx+c\)
(b) \({ e }^{ x }secx+c\)
(c) \({ e }^{ x }sinx+c\)
(d) \({ e }^{ x }tanx+c\)
Solution:
NCERT Maths Solutions for Class 12 Ex 7.6 Q 24

NCERT Solutions for Class 12 Maths Integrals Exercise 7.6 in Hindi

प्रश्न 1 से 22 तक के प्रश्नों के फलनों का समाकलन कीजिए

प्रश्न 1.
फलन x sin x का x के सापेक्ष समाकल ज्ञात कीजिए।
हल-
∫x sin x dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 in PDF
= – x cos x + ∫cos x dx
= – x cos x + sin x + C

प्रश्न 2.
x sin 3x
हल-
माना I = ∫x.sin 3x dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 in English Medium

प्रश्न 3.
x2 ex
हल-
माना I = ∫x2 ex dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 for up board

प्रश्न 4.
फलन x log x का x के सापेक्ष समाकल ज्ञात कीजिए।
हल-
∫ x log x dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 cbse board

प्रश्न 5.
x log 2x
हल-
माना I = ∫x log 2x dx
= ∫(log 2x).x dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 for mp board

प्रश्न 6.
फलन x² log x का x के सापेक्ष समाकल ज्ञात कीजिए।
हल-
माना I = ∫x² log x dx
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 for gujrat board

प्रश्न 7.
x sin-1 x
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 for 2019-20

प्रश्न 8.
x tan-1x
हल-
12th Maths 7.6

प्रश्न 9.
x cos-1 x
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 free guide

प्रश्न 10.
(sin-1x)2
हल-
माना I = [(sin-1 x)2 dx ….(1)
sin-1 x = θ ⇒ x = sinθ ⇒ dx = cos θ dθ
∴(1) से,
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 in Hindi Medium

प्रश्न 11.
12th Maths 7.6 sols
हल-
12 Maths 7.6

प्रश्न 12.
x sec² x
हल-
माना I = ∫x sec² x dx
7.6 sols
x को पहला फलन तथा sec²x को दूसरा फलन लेकन खण्डश: समाकलन करने पर,
= x tan x – ∫1. tan x dx
= x tan x + log|cos x| + C

प्रश्न 13.
tan-1 x
हल-
7.6 sols maths

प्रश्न 14.
x(log x)²
हल-
माना I = ∫x (log x)² dx
= ∫(log x)².x dx
Exercise 7.6 sols class 12th maths
12 Maths 7.6 solutions in hindi

प्रश्न 15.
(x² + 1) log x
हल-
माना I = ∫(x² + 1) log x dx
= ∫log x. (x² + 1) dx
(log x) को पहला फलन तथा (x² + 1) को दूसरा फलन लेकर खण्डश: समाकलन करने पर,
7.6 class 12

प्रश्न 16.
e(sinx + cosx)
हल-
ex sinx = t
⇒ e(sinx + cosx)dx = dt
= ∫ex(sinx + cosx)dx = ∫dt = t + c
= ex sinx + c

प्रश्न 17
7.6 integrations
हैल-
7.6 solutions
ncert solution of class 12 maths

प्रश्न 18.
maths integration class 12
हल-
ncert maths solutions class 12 chapter 7

प्रश्न 19.
class 12 ncert maths solutions
हल-
integration class 12 pdf

प्रश्न 20.
UP Board Solutions for Class 12 Maths Chapter 7 Integrals 20
हल-
maths ncert solution class 12

प्रश्न 21.
e2x sinx
हल-
ncert class 12 maths solutions pdf

प्रश्न 22.
properties of definite integrals class 12
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.6

प्रश्न 23
UP Board Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.6
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integration

प्रश्न 24.
UP Board Solutions for Class 12 Maths Chapter 7 Ex 7.6
हल-
UP Board Solutions for Class 12 Maths Chapter 7 Integration Exercise 7.6