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# Class 12 RD Sharma Solutions – Chapter 20 Definite Integrals – Exercise 20.3 | Set 1

• Last Updated : 14 Jul, 2021

### Question 1(i).

Solution:

We have,

I =

I =

I =

I =

I = 8 + 6 – 2 – 3 + 24 + 20 – 6 – 10

I = 37

### Question 1(ii).

Solution:

We have,

I =

I =

I =

I =

I =

I = 0 + 1 + 3 – π/2 + e6 – e0

I = 3 – π/2 + e6

### Question 1(iii).

Solution:

We have,

I =

I =

I =

I =

I =

I = 63/2 + 9 – 7/2 – 3 + 64 – 36

I = 56/2 + 34

I = 62

### Question 2.

Solution:

We have,

I =

We know that,

So, we get

I =

I =

I =

I = –2 + 4 – 8 – 8 + 8 + 8 – 2 + 4

I = 20

### Question 3.

Solution:

We have,

I =

We know that,

So, we get

I =

I =

I = 0 + 2 + 8 – 0

I = 10

### Question 4.

Solution:

We have,

I =

We know that,

So, we get

I =

I =

I = –1/4 + 1/2 + 1 – 1 + 1 + 1 – 1/4 + 1/2

I = 5/2

### Question 5.

Solution:

We have,

I =

We know that,

So, we get

I =

I =

I = –9/4 + 9/2 + 4 – 6 + 4 + 6 – 9/4 + 9/2

I = 25/2

### Question 6.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = 1/3 – 3/2 + 2 – [8/3 – 6 + 4 – 1/3 + 3/2 – 2]

I = 1/3 – 3/2 + 2 – 8/3 + 6 – 2 + 1/3 – 3/2

I = 1

### Question 7.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I = –1/6 + 1/3 – 0 + 27/2 + 3 – 1/6 – 1/3

I = 65/6

### Question 8.

Solution:

We have,

I =

We know that,

So, we get

I =

I =

I =

I = –2 + 4 + 18 – 12 + 18 + 12 – 2 + 4

I = 40

### Question 9.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = -1/2 + 1 + 2 – 2 + 2 + 2 – 1/2 + 1

I = 5

### Question 10.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = – 2 – 6 + 1/2 + 3

I = – 5 + 1/2

I = (-10 + 1)/2

I = -9/2

### Question 11.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = 1/2 – 0 – 0 + 1/2

I = 1

### Question 12.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = 1 + 1 + 1 – (–1)

I = 1 + 1 + 1 + 1

I = 4

### Question 13.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = 1 – 1/√2 – 1/√2 + 1

I = 2 – 2/√2

I = 2 – √2

### Question 14.

Solution:

We have,

I =

We know that,

So we get,

I =

I =

I =

I = – 25/2 + 25 + 2 – 10 + 32 – 40 – 25/2 + 25

I = 9

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