Chapter 4 Definite Integration Ex 4.2

I. Evaluate: Question 1.Solution: Question 2. Solution: Question 3. Solution:The integral does not exist since cot 0 is not defined. Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question 14. Solution: Question 15. … Read more

Chapter 3 Indefinite Integration Ex 3.4

I. Integrate the following w. r. t. x: Question 1.Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question 14. Question 15. Solution: Question 16. Solution: Question … Read more

Chapter 3 Indefinite Integration Ex 3.3

I. Evaluate the following: Question 1.∫ log x dxSolution: Question 2.∫ sin 3x dxSolution: Question 3.∫x  x dxSolution: Question 4.∫  x dxSolution: Question 5. Question 6. Question 7. Question 8.∫x . x dxSolution: Question 9.∫ log x dxSolution: Question 10.∫ cos 3x dxSolution: Question 11.∫x  x dxSolution: Question 12.∫  x dxSolution: Question 13. Solution:= t(log t – 1) + c= (log … Read more

Chapter 3 Indefinite Integration Ex 3.2(C)

I. Evaluate: Question 1. Question 2. Question 3. Question 4. Question 5. 7x + 3 = A(2 – 2x) + B∴ 7x + 3 = -2Ax + (2A + B)Comparing the coefficient of x and constant on both the sides, we get-2A = 7 and 2A + B = 3 Question 6. Solution:Comparing the coefficients … Read more

Chapter 3 Indefinite Integration Ex 3.2(B)

I. Evaluate the following: Question 1.Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question 14. Solution: Question 15. Solution: Question 16. Solution: Question 17. Solution: Question … Read more

Chapter 3 Indefinite Integration Ex 3.2(A)

I. Integrate the following functions w.r.t. x: Question 1.Solution: Question 2. Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13.Dividing numerator and denominator by cos2x, we get Question 14. Solution: Question 15. … Read more

Chapter 3 Indefinite Integration Ex 3.1

I. Integrate the following functions w.r.t. x: (i)  +  – x + 1Solution: Solution: Solution: Solution: Solution: II. Evaluate: (i) ∫ta x . dxSolution: Solution: Solution: Solution: Solution: = -cot x – tan x + c Solution: Solution: Solution: Solution: (x) ∫sin 4x cos 3x dxSolution: III. Evaluate: (i) ∫⋅dxSolution: Solution: Solution: Solution: Solution: Solution: Solution: (viii) … Read more