RD Sharma Class 12 Solutions - Indefinite Integrals - 1 | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


19. Indefinite Integrals
Exercise 19.2
1. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula,
? + +
2. Question
Evaluate the following integrals:
Answer
Given:
By Splitting them, we get,
By using the formula,
Page 2


19. Indefinite Integrals
Exercise 19.2
1. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula,
? + +
2. Question
Evaluate the following integrals:
Answer
Given:
By Splitting them, we get,
By using the formula,
By using the formula,
?
By using the formula,
3. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula
Page 3


19. Indefinite Integrals
Exercise 19.2
1. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula,
? + +
2. Question
Evaluate the following integrals:
Answer
Given:
By Splitting them, we get,
By using the formula,
By using the formula,
?
By using the formula,
3. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula
4. Question
Evaluate the following integrals:
? (2 – 3x)(3 + 2x)(1 – 2x)dx
Answer
Given:
??(2 - 3x)(3 + 2x)(1 - 2x)dx
By multiplying,
?? (6 - 4x - 9x - 6x
2
) dx
?? (6 - 13x - 6x
2
) dx
By Splitting, we get,
??6dx -?13 x dx -?6x
2
 dx
By using the formulas,
We get,
5. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using formula,
By using the formula,
Page 4


19. Indefinite Integrals
Exercise 19.2
1. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula,
? + +
2. Question
Evaluate the following integrals:
Answer
Given:
By Splitting them, we get,
By using the formula,
By using the formula,
?
By using the formula,
3. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula
4. Question
Evaluate the following integrals:
? (2 – 3x)(3 + 2x)(1 – 2x)dx
Answer
Given:
??(2 - 3x)(3 + 2x)(1 - 2x)dx
By multiplying,
?? (6 - 4x - 9x - 6x
2
) dx
?? (6 - 13x - 6x
2
) dx
By Splitting, we get,
??6dx -?13 x dx -?6x
2
 dx
By using the formulas,
We get,
5. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using formula,
By using the formula,
By using the formula,
6. Question
Evaluate the following integrals:
Answer
Given:
By applying (a - b)
2
 = a
2
 - 2ab + b
2
After computing,
By Splitting, we get,
By applying the formulas:
We get,
I = 1/2 x
2
 + logx - 2x + c
Page 5


19. Indefinite Integrals
Exercise 19.2
1. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula,
? + +
2. Question
Evaluate the following integrals:
Answer
Given:
By Splitting them, we get,
By using the formula,
By using the formula,
?
By using the formula,
3. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using the formula
4. Question
Evaluate the following integrals:
? (2 – 3x)(3 + 2x)(1 – 2x)dx
Answer
Given:
??(2 - 3x)(3 + 2x)(1 - 2x)dx
By multiplying,
?? (6 - 4x - 9x - 6x
2
) dx
?? (6 - 13x - 6x
2
) dx
By Splitting, we get,
??6dx -?13 x dx -?6x
2
 dx
By using the formulas,
We get,
5. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,
By using formula,
By using the formula,
By using the formula,
6. Question
Evaluate the following integrals:
Answer
Given:
By applying (a - b)
2
 = a
2
 - 2ab + b
2
After computing,
By Splitting, we get,
By applying the formulas:
We get,
I = 1/2 x
2
 + logx - 2x + c
7. Question
Evaluate the following integrals:
Answer
Given:
Applying: (a + b)
3
 = a
3
 + b
3
 + 3ab
2
 + 3a
2
b
?
?
By Splitting, we get,
By applying formula,
8. Question
Evaluate the following integrals:
Answer
Given:
By Splitting, we get,