RD Sharma Class 12 Solutions - Indefinite Integrals - 2 | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


4. Question
Evaluate the following integrals:
Answer
let 
Let  ……(i)
? dx = dt
so,
 [using (i)]
5. Question
Evaluate the following integrals:
Answer
We have,
= 
Sol, 
Let x+3 =t
Page 2


4. Question
Evaluate the following integrals:
Answer
let 
Let  ……(i)
? dx = dt
so,
 [using (i)]
5. Question
Evaluate the following integrals:
Answer
We have,
= 
Sol, 
Let x+3 =t
Then dx = dt
Exercise 19.16
1. Question
Evaluate the following integrals:
Answer
let 
Let tan x = t .....(i)
? dx = dt
so,
 [using (i)]
2. Question
Evaluate the following integrals:
Answer
: let 
Let  = t .....(i)
? dx = dt
so,
 [using(i)]
Page 3


4. Question
Evaluate the following integrals:
Answer
let 
Let  ……(i)
? dx = dt
so,
 [using (i)]
5. Question
Evaluate the following integrals:
Answer
We have,
= 
Sol, 
Let x+3 =t
Then dx = dt
Exercise 19.16
1. Question
Evaluate the following integrals:
Answer
let 
Let tan x = t .....(i)
? dx = dt
so,
 [using (i)]
2. Question
Evaluate the following integrals:
Answer
: let 
Let  = t .....(i)
? dx = dt
so,
 [using(i)]
3. Question
Evaluate the following integrals:
Answer
Let
Let sin x = t .....(i)
? cos x dx = dt
So, 
Again, let t + 2 = u …..(ii)
? dt = du
 [using(i),(ii)]
4. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
Let  .....(i)
Page 4


4. Question
Evaluate the following integrals:
Answer
let 
Let  ……(i)
? dx = dt
so,
 [using (i)]
5. Question
Evaluate the following integrals:
Answer
We have,
= 
Sol, 
Let x+3 =t
Then dx = dt
Exercise 19.16
1. Question
Evaluate the following integrals:
Answer
let 
Let tan x = t .....(i)
? dx = dt
so,
 [using (i)]
2. Question
Evaluate the following integrals:
Answer
: let 
Let  = t .....(i)
? dx = dt
so,
 [using(i)]
3. Question
Evaluate the following integrals:
Answer
Let
Let sin x = t .....(i)
? cos x dx = dt
So, 
Again, let t + 2 = u …..(ii)
? dt = du
 [using(i),(ii)]
4. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
Let  .....(i)
? dt = du
so,
 [using (i)]
 [using (ii)]
5. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
 [using (i)]
6. Question
Page 5


4. Question
Evaluate the following integrals:
Answer
let 
Let  ……(i)
? dx = dt
so,
 [using (i)]
5. Question
Evaluate the following integrals:
Answer
We have,
= 
Sol, 
Let x+3 =t
Then dx = dt
Exercise 19.16
1. Question
Evaluate the following integrals:
Answer
let 
Let tan x = t .....(i)
? dx = dt
so,
 [using (i)]
2. Question
Evaluate the following integrals:
Answer
: let 
Let  = t .....(i)
? dx = dt
so,
 [using(i)]
3. Question
Evaluate the following integrals:
Answer
Let
Let sin x = t .....(i)
? cos x dx = dt
So, 
Again, let t + 2 = u …..(ii)
? dt = du
 [using(i),(ii)]
4. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
Let  .....(i)
? dt = du
so,
 [using (i)]
 [using (ii)]
5. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
 [using (i)]
6. Question
Evaluate the following integrals:
Answer
let 
Let  = t .....(i)
? dx = dt
 [using (i)]
7. Question
Evaluate the following integrals:
Answer
Let 
Let  = t .....-----(i)
? 2x dx = dt
Put t + 1 = u .....-----(ii)
? dt = du