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NCERT Solutions for Class 12 Maths Chapter 7 Integrals

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NCERT Solutions for Class 12 Maths Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Chapter 7  Integrals: Engineering aspirants and students appearing for CBSE Class 12 board exams must take the NCERT Mathematics textbooks seriously and finish them from top to bottom. They must also go through the NCERT solutions for Class 12 Maths and Class 11 Maths to have a better understanding of the various concepts. In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 7 – Integrals which have been designed by the best teachers in India.

Class 12 Maths Chapter 7 NCERT Solutions Integrals

NCERT Solutions for Class 12 Maths Chapter 7 – Integrals contains step-by-step and detailed solutions for every question. The topics and sub-topics included in the Integrals chapter are the following:

  1. Introduction
  2. Integration as an Inverse Process of Differentiation
  3. Geometrical interpretation of indefinite integral
  4. Some properties of indefinite integral
  5. Comparison between differentiation and integration
  6. Methods of Integration
  7. Integration by substitution
  8. Integration using trigonometric identities
  9. Integrals of Some Particular Functions
  10. Integration by Partial Fractions
  11. Integration by Parts
  12. Integral of the type
  13. Integrals of some more types
  14. Definite Integral
  15. Definite integral as the limit of a sum
  16. Fundamental Theorem of Calculus
  17. Area function
  18. First fundamental theorem of integral calculus
  19. Second fundamental theorem of integral calculus
  20. Evaluation of Definite Integrals by Substitution
  21. Some Properties of Definite Integrals

Question 1.
sin 2x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 1
Question 2.
cos 3x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 2
Question 3.
{ e }^{ 2x }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 3
Question 4.
(ax + c)²
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 4
Question 5.
{ sin\quad 2x-4e }^{ 3x }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 5
Find the following integrals in Exercises 6 to 20 :

Question 6.
\int { \left( { 4e }^{ 3x }+1 \right) dx }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 6
Question 7.
\int { { x }^{ 2 }\left( 1-\frac { 1 }{ { x }^{ 2 } } \right) dx }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 7
Question 8.
\int { { (ax }^{ 2 }+bx+c)dx }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 8
Question 9.
\int { \left( { 2x }^{ 2 }+{ e }^{ x } \right) dx }
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 9
Question 10.
\int { { \left[ \sqrt { x } -\frac { 1 }{ \sqrt { x } } \right] }^{ 2 }dx }
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 10
Question 11.
\int { \frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx }
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 11
Question 12.
\int { \frac { { x }^{ 3 }+3x+4 }{ \sqrt { x } } dx }
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 12
Question 13.
\int { \frac { { x }^{ 3 }-{ x }^{ 2 }+x-1 }{ x-1 } dx }
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 13
Question 14.
\int { \left( 1-x \right) \sqrt { x } dx }
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.1 Q 14
Question 15.
\int { \sqrt { x } \left( { 3x }^{ 2 }+2x+3 \right) dx }
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.1 Q 15
Question 16.
\int { (2x-3cosx+{ e }^{ x })dx }
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 16
Question 17.
\int { \left( { 2x }^{ 2 }-3sinx+5\sqrt { x } \right) dx }
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 17
Question 18.
\int { secx(secx+tanx)dx }
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 18
Question 19.
\int { \frac { { sec }^{ 2 }x }{ { cosec }^{ 2 }x } dx }
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 19
Question 20.
\int { \frac { 2-3sinx }{ { cos }^{ 2 }x } dx }
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 20

Choose the correct answer in Exercises 21 and 22.
Question 21.
The antiderivative \left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right) equals
(a) \frac { 1 }{ 3 } { x }^{ \frac { 1 }{ 3 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c
(b) \frac { 2 }{ 3 } { x }^{ \frac { 2 }{ 3 } }+{ \frac { 1 }{ 2 } x }^{ 2 }+c
(c) \frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c
(d) \frac { 3 }{ 2 } { x }^{ \frac { 3 }{ 2 } }+\frac { 1 }{ 2 } { x }^{ \frac { 1 }{ 2 } }+c
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 21
Question 22.
If \frac { d }{ dx } f(x)={ 4x }^{ 3 }-\frac { 3 }{ { x }^{ 4 } } such that f(2)=0 then f(x) is
(a) { x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } -\frac { 129 }{ 8 }
(b) { x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } +\frac { 129 }{ 8 }
(c) { x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } +\frac { 129 }{ 8 }
(d) { x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } -\frac { 129 }{ 8 }
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 22

Updated NCERT Solutions for Class 12 Maths for 2019 Exams.

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Comments

  11. This site of yours has quite proved a helping hand for me in almost my every examination….Every solution is vivid…thanku

    Reply

  13. Thanks, man. Very helpful. I don’t even know how many times I have been on this website now for revision

    Reply

  29. This site is like a doubt teacher mean every question is there with correct and proper answers. thanks a lot man.

    Reply

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