Table of Contents
Chapter 20 Definite Integrals Exercise Ex. 20.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
Evaluate the Integral in using substitution.
Solution 44
Question 45
Solution 45
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50
Question 51
Solution 51
Question 52
Solution 52
Question 54
Solution 54
Question 55
Solution 55
Question 56
Solution 56
Let cosx =u , Then
Hence
Question 57
Solution 57
Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60
Given :
Question 61
Solution 61
Question 62
Solution 62
Question 63
Solution 63
Question 64
Solution 64
We know , By reduction formula
For n=2
For n=4
Hence
Note: Answer given at back is incorrect.Question 65
Solution 65
Using Integration By parts
Question 66
Solution 66
Question 67
Solution 67
Note: Answer given in the book is incorrect. Question 68
Solution 68
=(1/4)log(2e)
Chapter 20 Definite Integrals Exercise Ex. 20.2
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Using Integration By parts
Hence
Question 25
Solution 25
Question 26
Solution 26
Question 27
Evaluate Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
?Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
Solution 44
Question 45
Solution 45
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50
Question 51
Solution 51
Question 52
Solution 52
Question 53
Solution 53
Question 54
Solution 54
Question 55
Solution 55
Question 56
Solution 56
Question 57
Solution 57
Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60
Question 61
Solution 61
Question 62
Solution 62
Chapter 20 Definite Integrals Exercise Ex. 20.3
Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
2x+3 is positive for x>-1.5 . Hence
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Evaluate the integral Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
For
Using Integration By parts
For
Using Integration By parts
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 27
Solution 27
[x]=0 for 0 < x
and [x]=1 for 1< x < 2
Hence
Question 28
Solution 28
Question 26
Evaluate the following integrals:
Solution 26
NOTE: Answer not matching with back answer.
Chapter 20 Definite Integrals Exercise Ex. 20.4A
Question 1
Solution 1
We know
Hence
We know
If
Then also
Hence
Question 2
Solution 2
We know
Hence
If
Then
Question 3
Solution 3
We know
Hence
If
Then
So
Question 4
Solution 4
We know
Hence
If
Then
Hence
Question 5
Solution 5
We know
Hence
If
Then
So
We know
If f(x) is even
If f(x) is odd
Here
f(x) is even, hence
Note: Answer given in the book is incorrect.Question 6
Solution 6
We know
Hence
If
Then
So
Question 7
Solution 7
We know
Hence
If
Then
So
Question 8
Solution 8
We know
Hence
If
Then
So
Note: Answer given in the book is incorrect. Question 9
Solution 9
If f(x) is even
If f(x) is odd
Here
is odd and
is even. Hence
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Chapter 20 Definite Integrals Exercise Ex. 20.4B
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
BQuestion 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Hence
Question 20
Solution 20
Question 21
Solution 21
Now
Let cosx=t
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25 (i)
Solution 25 (i)
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32 (i)
Solution 32 (i)
Question 33
Solution 33
Question 34
Evaluate the integral Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
We know
Also here
So
Hence
Question 39
Solution 39
Question 43
Solution 43
Question 44
Solution 44
Question 45
Solution 45
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Chapter 20 Definite Integrals Exercise Ex. 20RE
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Evaluate the following integrals
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Evaluate the integral Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Evaluate the following integrals
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Evaluate the following integrals
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
Solution 44
Question 45
Solution 45
Question 46
Solution 46
Question 47
Solution 47
Question 48
Solution 48
Question 49
Solution 49
Question 50
Solution 50
Question 51
Solution 51
Question 52
Solution 52
Question 53
Solution 53
Question 54
Solution 54
Question 55
Solution 55
Question 56
Solution 56
Question 57
Solution 57
Question 58
Solution 58
Question 59
Solution 59
Question 60
Solution 60
Question 61
Solution 61
Question 62
Solution 62
Question 63
Solution 63
Question 64
Solution 64
Question 65
Solution 65
Question 66
Solution 66
Question 67
Solution 67
Question 68
Solution 68
Question 69
Solution 69
Chapter 20 Definite Integrals Exercise Ex. 20.5
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Evaluate the following in tegrals as limit of sums
Solution 31
Question 32
Evaluate the following in tegrals as limit of sums
Solution 32
Question 33
Solution 33
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