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# Class 12-science RD SHARMA Solutions Maths Chapter 20 - Definite Integrals

## Definite Integrals Exercise Ex. 20.1

### Solution 56

Let cosx =u , Then

Hence

Given :

### 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 67

Note: Answer given in the book is incorrect.

=(1/4)log(2e)

## Definite Integrals Exercise Ex. 20.2

### Solution 24

Using Integration By parts

Hence

## Definite Integrals Exercise Ex. 20.3

### Solution 5

2x+3 is positive for x>-1.5 . Hence

### Solution 21

For

Using Integration By parts

For

Using Integration By parts

### Solution 27

[x]=0 for 0 < x

and [x]=1 for 1< x < 2

Hence

## Definite Integrals Exercise Ex. 20.4A

We know

Hence

We know

If

Then also

Hence

We know

Hence

If

Then

We know

Hence

If

Then

So

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.

We know

Hence

If

Then

So

We know

Hence

If

Then

So

### Solution 8

We know

Hence

If

Then

So

Note: Answer given in the book is incorrect.

If f(x) is even

If f(x) is odd

Here

is odd and

is even. Hence

B

Hence

Now

Let cosx=t

We know

Also here

So

Hence

## Definite Integrals Exercise MCQ

### Solution 1

Correct option: (d)

### Solution 2

Correct option: (c)

### Solution 3

Correct option: (a)

### Solution 4

Correct option: (c)

### 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 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)

### Solution 34

Correct option:(d)

### Solution 35

Correct option: (c)

### Solution 36

Correct option: (a)

### Solution 37

Correct option:(d)

### 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)