## 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) a^{2} 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

= ∫sec^{2} 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.

∫ tan^{2} x dx

Solution :

∫ tan^{2} x dx = ∫ (sec^{2} x – 1) dx

= ∫ sec^{2} x – ∫ dx

= tan x – x + C

Question 13.

∫ cot^{2} x dx

Solution :

∫ (cosec^{2} x – 1) dx

= ∫ cosec^{2} x dx – ∫dx

= – cot x – x + C

Question 14.

Solution :

Question 15.

∫ (tan^{2} x – cot^{2} x) dx

Solution :

∫ (tan^{2} x – cot^{2} x) dx

= ∫ (sec^{2} x -1 – cosec^{2} x +1) dx

= ∫ sec^{2} x dx – ∫ cosec^{2} 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.

∫ log_{x} x dx

Solution :

Question 22.

Solution :

Question 23.

Solution :

Question 24.

Solution :

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