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## NCERT Solutions class 12 Maths Integrals

Integrate the function in Exercises 1 to 11.

1.

Ans. Let I =

Here,

=

=

= ……….(i)

Comparing the coefficients of  –A + B – C = 0 ……….(ii)

Comparing the coefficients of  B + C = 0 ……….(iii)

Comparing constants A = 1 ……….(iv)

On solving eq. (ii), (iii) and (iv), we get  A = 1, B =  C =

Putting these values in eq. (i),

=

=

=

=

=

=

=

Ans. Let I =

=

=

=

=

=

=

=

=

### 3.

Ans. Let I =  ……….(i)

Putting

From eq. (i),

I =

=

=

=

=

=

Ans. Let I =

=

=

Putting

I =

=

=

Ans. Let I =

Putting

I =

=

=

=

=

=

=

=

=

=

### 6.

Ans. Let I =  ……….(i)

Let  ……….(ii)

Comparing coefficients of  A + B = 0 ……….(iii)

Comparing coefficients of  B + C = 5 ……….(iv)

Comparing constants 9A + C = 0 ……….(v)

On solving eq. (iii), (iv) and (v), we get  A =  B =  C =

Putting these values of A, B and C in eq. (ii),

From eq. (i),

I =

=

=

=

Ans. Let I =

=

=

=

=

=

=

=

=

Ans. Let I =

=

=

=

I =

=

### 9.

Ans. Let I =  ……….(i)

Putting

From eq. (i),

I =

=

=

10.

Ans. Let I =  ……….(i)

I =

=

I =

I =

I =

=

I =

=

11.

Ans. Let I = ……….(i)

I =

=

I =

I =

I =

I =

I =

Integrate the function in Exercises 12 to 22.

12.

Ans. Let I =

=  ……….(i)

Putting

From eq. (i),

I =

=

=

13.

Ans. Let I =  ……….(i)

Putting

From eq. (i), I =

=  ……….(ii)

I =

=

I =

=

I =

=

14.

Ans. Let I =  ……….(i)

I =

=

I =

=

I =  +c

15.

Ans. Let I =

=

= ……….(i)

Putting

From eq. (i),

I =

=

=

Ans. Let I =

=

=

=

I =

Putting

From eq. (i),

I =

=

I =

=

Ans. Let I =

=  ………..(i)

Putting

From eq. (i),

I =

= if

And I =

=

=  if

I =  if

And I = if

Ans. Let I =

=

I =

=

I =

Putting

I =

=

=

I =

=

I =

=

### 19.

Ans. We know that

I =

=

I =

= ……….(i)

Putting

=

I =

=

I =

[Applying product rule]

I =

I =

I =

Putting

I =

I =

I =

### 20.

Ans. Let I =

Putting

I =

=

=

=

I = ……….(i)

I =

=

I =

I =  ……….(ii)

For evaluating , putting

=

=

=

= ……….(iii)

Putting this value in eq. (ii),

I =

I =

=

I =

21.

Ans. Let I =

=

=

=

=

=

=

NCERT Solutions class 12 Maths Miscellaneous Part 1

### 22.

Ans. Let I =  ……….(i)

Let  ……….(ii)

Comparing coefficients of  A + C = 1 ……….(iii)

Comparing coefficients of  3A + B + 2C = 1  ……….(iv)

Comparing constants 2A + 2B + C = 1  ……….(v)

On solving eq. (iii), (iv) and (v), we get  A = –2, B = 1, C = 3

Putting these values of A, B and C in eq. (ii),

=

=

=

=

## NCERT Solutions class 12 Maths Miscellaneous Part 1

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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