ECAT Mathematics Integration Online Test

2. – ∫ sec²x/cotx dx – ∫ cosec²x/cotx dx =

3. ∫ 1/1+x² dx =

4. ∫ (Tan⁴ x + Tan² x) dx = ?

5. ∫ a/xⁿ dx ?

6. In 2 ∫ 2ˣ dx =

7. ∫ 2x – 1/x²–x+1 dx =

8. If n ≠ – 1. Then ∫ [f(x)]ⁿ f’(x)(dx) =

9. ∫ d/dx (x² + 3x) dx =

10. ∫ dx/xsin²(ln x) = ?

11. The integration is the reverse process of

12. ∫ cos xdx/sin x In sin x = ?

14. Solution of differential equation dy/dx = sinx/siny = 0

15. ∫ [eˣ - sin2x/cos²x]dx = ?

16. ∫(eˣ + cosc) = dx

18. The area bounded by x – axis and the curve y = 4x – x² is

19. 6/(x³ – 3x²)⁶ ∫ (x³ – 3x²)⁵ (3x² – 6x) dx =

20. If Ø’ (x) = f(x), then Ø (x) is called

21. ∫ dx/√a² – x² =

22. ∫ -1/x√x² - 1 dx =

23. ∫ Tanxdx/In sec x = ?

24. ∫ 6(x³ – 3x²)⁵ (3x² – 6x)dx = ?

25. The slope of tangent to the curve y = x² - 2x at P(1,1) is

26. ∫ eˣ [sinh⁻¹ x + 1/√1+x²] dx = ?

28. ∫ 2x+5/x²+5x dx

29. ∫ dx/x² – a² =

30. ∫ dx/√a² – x² = ?

32. ∫sin xdx =

33. ∫ dX/X² – 9 = ?

34. ∫ - 3cosec² 3xdx =

35. Solution of differential equation dy/dx = 1/√1 – x² is

36. In a ∫ aˣ dx =

37. ∫(∫ 1/x sec² x/Tanx)dx

38. ∫ –2x/√4 – x² dx

39. ∫(1/x + cosec²x/cotx) dx =

40. ∫(√x – 1/√x)² dx =

41. ∫ cot xdx =

42. The general solution of differential equation of order 40 is that solution which contains __________ essential arbitrary constants.

43. ∫ 1/1+x² dx =

44. Suitable substitution to integrate √x²–a² is

45. ∫ 1/xInx dx =

46. ∫(eˣ - sin2x/cos²x) dx =

47. If y = f(x), then f(x + sx) is nearly equal to

49. ∫ sin⁻¹ (cos)dx = ?

50. ∫ - 2cosec² 2xdx =