Class 12 RD Sharma Solutions – Chapter 20 Definite Integrals – Exercise 20.3 | Set 1
Evaluate the following integrals:
Question 1(i).
Solution:
We have,
I =
I =
Using additive property, we get
I =
I =
I = 8 + 6 – 2 – 3 + 24 + 20 – 6 – 10
I = 37
Question 1(ii).
Solution:
We have,
I =
I =
Using additive property, we get
I =
I =
I =
I = 0 + 1 + 3 – π/2 + e6 – e0
I = 3 – π/2 + e6
Question 1(iii).
Solution:
We have,
I =
I =
Using additive property, we get
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
Last Updated :
14 Jul, 2021
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