NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 7

Integrals Class 12

Chapter 7 Integrals Exercise 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11, miscellaneous Solutions

<< Previous Chapter 6 : Application of Derivatives Next Chapter 8 : Application of Integrals >>

Exercise 7.1 : Solutions of Questions on Page Number : 299

Q1 :  

sin 2x


Answer :

The anti derivative of sin 2x is a function of x whose derivative is sin 2x.

It is known that,

Therefore, the anti derivative of

Answer needs Correction? Click Here

Q2 :  

Cos 3x


Answer :

The anti derivative of cos 3x is a function of x whose derivative is cos 3x.

It is known that,

Therefore, the anti derivative of .

Answer needs Correction? Click Here

Q3 :  

e2x


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Q21 :  

The anti derivative of equals

(A) (B)

(C) (D)


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Q22 :  

If such that f(2) = 0, then f(x) is

(A) (B)

(C) (D)


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Exercise 7.2 : Solutions of Questions on Page Number : 304

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Q4 :  

sin x â‹… sin (cos x)


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Q29 :  

cot x log sin x


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Q38 :  

equals


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Q39 :  

equals


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Exercise 7.3 : Solutions of Questions on Page Number : 307

Q1 :  


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Q2 :  


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Q3 :  

cos 2x cos 4x cos 6x


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Q4 :  

sin3 (2x + 1)


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Q5 :  

sin3 x cos3 x


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Q6 :  

sin x sin 2x sin 3x


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Q7 :  

sin 4x sin 8x


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Q10 :  

sin4 x


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Q11 :  

cos4 2x


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Q16 :  

tan4x


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Q21 :  

sin-1 (cos x)


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Q23 :  

is equal to

A. tan x + cot x + C

B. tan x + cosec x + C

C. - tan x + cot x + C

D. tan x + sec x + C


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Q24 :  

equals

A. - cot (exx) + C

B. tan (xex) + C

C. tan (ex) + C

D. cot (ex) + C


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Exercise 7.4 : Solutions of Questions on Page Number : 315

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Q11 :  

19x2+


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Q23 :  

equals

A. x tan - 1 (x + 1) + C

B. tan - 1 (x + 1) + C

C. (x + 1) tan - 1 x + C

D. tan - 1x + C


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Q24 :  

equals

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B.

C.

D.


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Exercise 7.5 : Solutions of Questions on Page Number : 322

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Q16 :  

[Hint: multiply numerator and denominator by xn - 1 and put xn = t]


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Q17 :  

[Hint: Put sin x = t]


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Q21 :  

[Hint: Put ex = t]


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Q22 :  

A.

B.

C.

D.


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Q23 :  

A.

B.

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D.


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Exercise 7.6 : Solutions of Questions on Page Number : 327

Q1 :  

x sin x


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Q4 :  

x logx


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Q5 :  

x log 2x


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Q6 :  

x2 log x


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Q23 :  

equals


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Q24 :  

equals


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Exercise 7.7 : Solutions of Questions on Page Number : 330

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Q10 :  

is equal to

A.

B.

C.

D.


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is equal to

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B.

C.

D.


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Exercise 7.8 : Solutions of Questions on Page Number : 334

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Exercise 7.9 : Solutions of Questions on Page Number : 338

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Q21 :  

equals

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B.

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equals

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Exercise 7.10 : Solutions of Questions on Page Number : 340

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Q17 :  

The value of the integral is

A. 6

B. 0

C. 3

D. 4


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Q18 :  

The value of the integral is

A. 6

B. 0

C. 3

D. 4


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Q19 :  

If

A. cos x + x sin x

B. x sinx

C. x cos x

D. sin x + x cos x


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Q20 :  

If

A. cos x + x sin x

B. x sinx

C. x cos x

D. sin x + x cos x


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Exercise 7.11 : Solutions of Questions on Page Number : 347

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Q36 :  

Show that if f and g are defined as and


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Q37 :  

Show that if f and g are defined as and


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Q38 :  

The value of is

A. 0

B. 2

C. π

D. 1


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Q39 :  

The value of is

A. 0

B. 2

C. π

D. 1


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The value of is

A. 2

B.

C. 0

D.


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Q41 :  

The value of is

A. 2

B.

C. 0

D.


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Exercise Miscellaneous : Solutions of Questions on Page Number : 352

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[Hint: Put]


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Q40 :  

Evaluate as a limit of a sum.


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Q41 :  

is equal to

A.

B.

C.

D.


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is equal to

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B.

C.

D.


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Q43 :  

If then is equal to

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B.

C.

D.


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Q44 :  

The value of is

A. 1

B. 0

C. - 1

D.


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<< Previous Chapter 6 : Application of Derivatives Next Chapter 8 : Application of Integrals >>

Maths Part-2 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Integrals ( Exercise 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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Exercise 7.1
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Exercise 7.2
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
Question 30
Question 31
Question 32
Question 33
Question 34
Question 35
Question 36
Question 37
Question 38
Question 39
Exercise 7.3
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Exercise 7.4
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Exercise 7.5
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Exercise 7.6
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Exercise 7.7
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Exercise 7.8
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Exercise 7.9
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Exercise 7.10
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Exercise 7.11
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
Question 30
Question 31
Question 32
Question 33
Question 34
Question 35
Question 36
Question 37
Question 38
Question 39
Question 40
Question 41
Exercise Miscellaneous
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
Question 30
Question 31
Question 32
Question 33
Question 34
Question 35
Question 36
Question 37
Question 38
Question 39
Question 40
Question 41
Question 42
Question 43
Question 44