RBSE Solutions for Class 12 Maths Chapter 9 Integration Ex 9.1

Rajasthan Board RBSE Class 12 Maths Chapter 9 Integration Ex 9.1

Question 1.
Integrate the following with respect to x :
(a) 3 $x\sqrt { { x }^{ 2 } }$
(b) e^3x
(c) ( $\frac { 1 }{ 2 }$ )^x
(d) a² log_a x
Solution:

Find the value of the integrates given below :

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.
∫a^x da
Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.
∫sec x (sec x + tan x) dx
Solution:
∫sec x (sec x + tan x) dx
= ∫sec² x dx + ∫sec x tan x dx
= tan x + sec x + C

Question 10.
∫(sin^-1 x + cos^-1 x) dx
Solution :

Question 11.

Solution :

Question 12.
∫ tan² x dx
Solution :
∫ tan² x dx = ∫ (sec² x – 1) dx
= ∫ sec² x – ∫ dx
= tan x – x + C

Question 13.
∫ cot² x dx
Solution :
∫ (cosec² x – 1) dx
= ∫ cosec² x dx – ∫dx
= – cot x – x + C

Question 14.

Solution :

Question 15.
∫ (tan² x – cot² x) dx
Solution :
∫ (tan² x – cot² x) dx
= ∫ (sec² x -1 – cosec² x +1) dx
= ∫ sec² x dx – ∫ cosec² x dx
= tan x + cot x + C

Question 16.

Solution :

Question 17.

Solution :

Question 18.

Solution :

Question 19.
∫ cot x (tan x – cosec x) dx
Solution :
∫ cot x (tan x – cosec x) dx
= ∫ cot x tan x dx – ∫ cot x cosec x dx
= ∫ 1 dx – ∫ cosec x cot x dx
= x + cosec x + C

Question 20.

Solution :