Mathematics Integration Online Test

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Question 1

1. ∫ -1/x√x² - 1 dx =

Answer

sin⁻¹ x + c

Answer

cosec⁻¹ x + c

Answer

sec⁻¹ x + c

Answer

tan ⁻¹ x + c

Question 2

2. ∫ (Tan⁴ x + Tan² x) dx = ?

Answer

Tan⁴ x/4

Answer

Tan⁵ x/5

Answer

None of these

Question 3

3. ∫ dX/X² – 9 = ?

Answer

None of these

Answer

1/9 Tan ⁻¹(x/9) + c

Answer

1/6 In x–3/x+3 + c

Answer

1/6 In x+3/x–3 + c

Question 4

4. 6/(x³ – 3x²)⁶ ∫ (x³ – 3x²)⁵ (3x² – 6x) dx =

Answer

(x³ – 3x²)⁶/6 + c

Answer

(x³ – 3x²)⁴/4 + c

Answer

(x³ – 3x²)⁶ + c

Question 5

5. ∫(eˣ - sin2x/cos²x) dx =

Answer

In(xcos²x) + c

Answer

In(ex cos²x) + c

Answer

In(xsinx) + c

Answer

In(xsin²x) + c

Question 6

6.

Question 7

7. ∫ dx/xsin²(ln x) = ?

Question 8

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

Answer

y = cotx + c

Answer

y = tan⁻¹ x + c

Answer

y = sec⁻¹ x

Answer

y = sin⁻¹ x + c

Question 9

9. ∫ - 3cosec² 3xdx =

Answer

tan 3x + c

Answer

-cos 3x + c

Answer

-cot3x + c

Answer

cot 3x + c

Question 10

10. ∫ dx/x² – a² =

Answer

½ In x+a/x–a + c

Answer

½ tan In (x/a) + c

Answer

½ In x–a/x+a + c

Answer

½ In a+x/a–x + c

Question 11

11. In 2 ∫ 2ˣ dx =

Answer

1/2ˣ In 2 + c

Answer

2ˣ/In 2 + c

Answer

In 2/2ˣ + c

Question 12

12. ∫sin xdx =

Answer

-cos x + c

Question 13

13. ∫ a/xⁿ dx ?

Answer

axⁿ⁻¹/1 – n

Answer

axⁿ⁻¹(n – 1) + c

Answer

(ax)ⁿ⁺¹

Answer

axⁿ⁺¹/n+1 + c

Question 14

14. ∫ 1/xInx dx =

Answer

In In x + c

Answer

In In In x + c

Question 15

15. ∫ cot xdx =

Answer

In cotx + c

Answer

In sinx + c

Answer

In secx + c

Answer

In cosecx + c

Question 16

16.

Question 17

17. ∫ 1/1+x² dx =

Answer

cos⁻¹ x + c

Answer

tan⁻¹ x + c

Answer

sin⁻¹ x + c

Answer

cot⁻¹ x + c

Question 18

18.

Question 19

19. ∫(1/x + cosec²x/cotx) dx =

Answer

In(xcotx)+c

Answer

In(xtanx)+c

Answer

Inx+tanx+c

Answer

Inx–cotx+c

Question 20

20.

Question 21

21. ∫ eˣ [sinh⁻¹ x + 1/√1+x²] dx = ?

Answer

eˣ tan⁻¹x + c

Answer

eˣ cos h⁻¹ x

Answer

eˣ sinh⁻¹ x + c

Answer

eˣ cos⁻¹ x + c

Question 22

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

Question 23

23. ∫ dx/√a² – x² = ?

Answer

Sin⁻¹ x/a + c

Answer

A sin⁻¹ x/a

Answer

1/a sin⁻¹ x/a

Answer

1/a Tan⁻¹ x/a

Question 24

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

Answer

f(x), f(sx)

Answer

y + s (x + sx)

Answer

f(x) + f(sx)

Question 25

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

Answer

Cos y – cos x = c

Answer

Sin x = sin y

Answer

Cos x = cos y

Answer

Sin x + sin y = c

Question 26

26. ∫ 6(x³ – 3x²)⁵ (3x² – 6x)dx = ?

Answer

(x³ – 3x²)⁶ + c

Answer

(x³ – 3x²)⁴/4 + c

Answer

(x³ – 3x²)⁶/6 + c

Answer

None of these

Question 27

27. ∫ dx/√a² – x² =

Answer

sin⁻¹ x + c

Answer

sin⁻¹(x/a) + c

Answer

cosh⁻¹(x/a) + c

Answer

sinh⁻¹(x/a) + c

Question 28

28. ∫ sin⁻¹ (cos)dx = ?

Answer

πx + x²/2

Answer

πx/2 – x²/2

Question 29

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

Answer

[f(x)]ⁿ⁻¹/n – 1 +c

Answer

[f(x)]ⁿ⁻¹/n +c

Answer

n[f(x)]ⁿ⁻¹ +c

Answer

[f(x)]ⁿ⁺¹/n + 1 +c

Question 30

30. ∫ [eˣ - sin2x/cos²x]dx = ?

Answer

In(x sin²x) + c

Answer

In(x sinx) + c

Answer

In(x cos²x) + c

Answer

In(eˣ cos² x) + c

Question 31

31. Suitable substitution to integrate √x²–a² is

Answer

x = a cot Ø

Answer

x = a tan Ø

Answer

x = a sin Ø

Answer

x = a sec Ø

Question 32

32. ∫ d/dx (x² + 3x) dx =

Answer

x³/3 + 3x²/2 + c

Answer

x² + 3x + c

Answer

2x + 3 + c

Question 33

33.

Question 34

34. In a ∫ aˣ dx =

Answer

1/aˣin a + c

Answer

in a/aˣ + c

Answer

aˣ/in a + c

Question 35

35. ∫ cos xdx/sin x In sin x = ?

Answer

In(In cos x) c

Answer

In sinx + c

Answer

In(In sinx) + c

Answer

Incosx + c

Question 36

36. ∫ –2x/√4 – x² dx

Answer

8 – 2x² + c

Answer

2√4–x² + c

Answer

2√x²–4 + c

Question 37

37.

Question 38

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

Question 39

39. ∫ - 2cosec² 2xdx =

Answer

-cos2x + c

Question 40

40. ∫ 1/1+x² dx =

Answer

cot⁻¹ x + c

Answer

cos⁻¹ x + c

Answer

sin⁻¹ x + c

Answer

-cot⁻¹ x + c

Question 41

41. ∫ 2x+5/x²+5x dx

Answer

In|x²+5x| + c

Answer

In|2x+5|+c

Question 42

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

Answer

Derivative of f(x)

Answer

Anti – derivatives

Answer

Derivatives of Ø

Answer

None of these

Question 43

43. The integration is the reverse process of

Answer

Tabulation

Answer

Differentiation

Answer

Classification

Answer

Sublimation

Question 44

44. ∫(∫ 1/x sec² x/Tanx)dx

Answer

In(x Tanx) + c

Answer

Inx – cot x + c

Answer

In (x cotx)

Answer

Inx – Tanx + c

Question 45

45. ∫(eˣ + cosc) = dx

Answer

ex – sin x + c

Answer

ex + sinx + c

Question 46

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

Answer

2 In cotx + c

Answer

In tanx + c

Answer

In cotx + c

Answer

2 In tanx + c

Question 47

47. ∫(√x – 1/√x)² dx =

Answer

½ x² + In x + c

Answer

x² – x + In x + c

Answer

½ x² – 2x + c

Answer

½ x² – 2x + In x + c

Question 48

48. ∫ Tanxdx/In sec x = ?

Answer

In(In cosx) + c

Answer

In (In cot x) + c

Answer

In (In tan x) + c

Answer

In(In sec x) + c

Question 49

49. ∫ 2x – 1/x²–x+1 dx =

Answer

(2x – 1) + c

Answer

In(x² – x + 1) + c

Answer

In(2x – 1) + c

Question 50

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

Question 51

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Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Mathematics Integration Online Test

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Maan Ali

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Important Math Integration Question and Answer

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Maan Ali

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