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) e3x
(c) (\(\frac { 1 }{ 2 } \))x
(d) a2 loga x
Solution:
Find the value of the integrates given below :
Question 2.
Solution:
Question 3.
Solution:
Question 4.
Solution:
Question 5.
Solution:
Question 6.
∫ax 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 :
Question 21.
∫ logx x dx
Solution :
Question 22.
Solution :
Question 23.
Solution :
Question 24.
Solution :
Leave a Reply