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