Chapter 3 Indefinite Integration Miscellaneous Exercise 3

I. Choose the correct options from the given alternatives:

Question 1.

Question 2.

word image 20470 3

Question 3.

(a) log(3x) – log(9x) + c
(b) log(x) – (log 3) . log(log 9x) + c
(c) log 9 – (log x) . log(log 3x) + c
(d) log(x) + log(3) . log(log 9x) + c
Answer:
(b) log(x) – (log 3) . log(log 9x) + c
word image 20470 5

word image 20470 6

Question 6.

word image 20470 8
word image 20470 9

Question 7.
word image 20470 10

Question 8.
word image 20470 11

Question 9.
word image 20470 12
word image 20470 13

Question 10.

Question 11.
word image 20470 15

Question 13.
word image 20470 16

Question 14.
word image 20470 17

Question 15.
word image 20470 18
(a) sin 2x + c
(b) cos 2x + c
(c) tan 2x + c
(d) 2 sin 2x + c
Answer:
(a) sin 2x + c

Question 16.
word image 20470 19
word image 20470 20

Question 17.

Question 18.
∫[sin(log x) + cos(log x)] . dx =

(a) x cos(log x) + c
(b) sin(log x) + c
(c) cos(log x) + c
(d) x sin(log x) + c
Answer:
(d) x sin(log x) + c

Question 19.
word image 20470 22
(a) tan x – x + c
(b) x + tan x + c
(c) x – tan x + c
(d) -x – cot x + c
Answer:
(c) x – tan x + c
word image 20470 23

Question 20.
word image 20470 24

word image 20470 25

II. Integrate the following with respect to the respective variable:

Question 1.

Solution:

word image 20470 27
word image 20470 28

Question 2.

Solution:

word image 20470 29

Question 3.

Solution:
word image 20470 31

Question 4.

Solution:

word image 20470 33
word image 20470 34

Question 5.

Solution:

word image 20470 36

Question 6.

Solution:

word image 20470 38

Question 7.
cos 3x cos 2x cos x
Solution:
word image 20470 39
word image 20470 40

Question 8.

Solution:

word image 20470 42
word image 20470 43

Question 9.

word image 20470 45

III. Integrate the following w.r.t. x:

Question 1.

Solution:

word image 20470 47

Question 2.

Solution:
word image 20470 49
word image 20470 50
word image 20470 51
word image 20470 52
word image 20470 53

Question 3.

Solution:

word image 20470 55

Question 4.

Solution:
word image 20470 57

Question 5.

Solution:
word image 20470 59
word image 20470 60

Question 6.

Solution:
word image 20470 62

Question 7.

Solution:

word image 20470 64

Question 8.

Solution:

word image 20470 66
word image 20470 67

Question 9.

Solution:

word image 20470 69
word image 20470 70
word image 20470 71
word image 20470 72

Question 10.

Solution:

word image 20470 74
word image 20470 75

Question 11.

Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q11
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q11.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q11.2

Question 12.

Solution:
word image 20470 81

Question 13.

Solution:

word image 20470 84

Question 14.

Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q14
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q14.1

Question 15.

Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q15
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q15.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q15.2

Question 16.

Solution:

word image 20470 93
word image 20470 94

Question 17.

Solution:

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q17
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q17.1

Question 18.

Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q18
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Miscellaneous Exercise 3 III Q18.1

Question 19.

Solution:

word image 20470 102

Question 20.

Solution:
word image 20470 104