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Home/Mathematics/Mathematics Integration Online Test

Mathematics Integration Online Test

Maan AliLast Updated: October 15, 2025

Important Math Integration Question and Answer

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

Math Integration Practice Test Online With Explanation

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Page 1 of 2

1. ∫ Tanxdx/In sec x = ?

In (In tan x) + c

In (In cot x) + c

In(In sec x) + c

In(In cosx) + c

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2. 6/(x³ – 3x²)⁶ ∫ (x³ – 3x²)⁵ (3x² – 6x) dx =

(x³ – 3x²)⁴/4 + c

(x³ – 3x²)⁶/6 + c

(x³ – 3x²)⁶ + c

c

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3. ∫ dx/x² – a² =

½ tan In (x/a) + c

½ In a+x/a–x + c

½ In x–a/x+a + c

½ In x+a/x–a + c

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4. ∫(1/x + cosec²x/cotx) dx =

In(xtanx)+c

Inx+tanx+c

In(xcotx)+c

Inx–cotx+c

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5. ∫(√x – 1/√x)² dx =

½ x² + In x + c

½ x² – 2x + In x + c

½ x² – 2x + c

x² – x + In x + c

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6. ∫ cot xdx =

In sinx + c

In cotx + c

In secx + c

In cosecx + c

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7. ∫ dx/√a² – x² = ?

1/a Tan⁻¹ x/a

A sin⁻¹ x/a

Sin⁻¹ x/a + c

1/a sin⁻¹ x/a

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8. ∫ -1/x√x² - 1 dx =

sec⁻¹ x + c

tan ⁻¹ x + c

cosec⁻¹ x + c

sin⁻¹ x + c

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9.

B

D

A

C

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

32/3

64/3

64

32

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11.

Math 17.04

A

B

D

C

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12. ∫ 2x – 1/x²–x+1 dx =

0

In(x² – x + 1) + c

In(2x – 1) + c

(2x – 1) + c

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13. ∫ - 2cosec² 2xdx =

Cot2x + c

-cos2x + c

Cos2x + c

Tan2x + c

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14. ∫ sin⁻¹ (cos)dx = ?

πx/2 – x²/2

x²/2

πx/2

πx + x²/2

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

Sin x + sin y = c

Cos x = cos y

Sin x = sin y

Cos y – cos x = c

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16. ∫ dx/xsin²(ln x) = ?

-tan(lnx)

-cot(lnx)

Tan (lnx)

Cot(lnx)

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17. ∫ d/dx (x² + 3x) dx =

x³/3 + 3x²/2 + c

x² + 3x + c

2x + 3 + c

2x + 3

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18. ∫ (Tan⁴ x + Tan² x) dx = ?

Tan⁴ x/4

Tan³x/3

Tan⁵ x/5

None of these

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19. Suitable substitution to integrate √x²–a² is

x = a sin Ø

x = a sec Ø

x = a tan Ø

x = a cot Ø

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

[f(x)]ⁿ⁺¹/n + 1 +c

[f(x)]ⁿ⁻¹/n +c

[f(x)]ⁿ⁻¹/n – 1 +c

n[f(x)]ⁿ⁻¹ +c

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

y = sec⁻¹ x

y = sin⁻¹ x + c

y = tan⁻¹ x + c

y = cotx + c

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22. ∫ 6(x³ – 3x²)⁵ (3x² – 6x)dx = ?

(x³ – 3x²)⁶ + c

(x³ – 3x²)⁶/6 + c

(x³ – 3x²)⁴/4 + c

None of these

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23. ∫ 1/1+x² dx =

cos⁻¹ x + c

sin⁻¹ x + c

cot⁻¹ x + c

tan⁻¹ x + c

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24. ∫(eˣ + cosc) = dx

Sinx + c

ex – sin x + c

ex + sinx + c

-sinx + c

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25. ∫ [eˣ - sin2x/cos²x]dx = ?

In(x cos²x) + c

In(x sinx) + c

In(x sin²x) + c

In(eˣ cos² x) + c

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Page 2 of 2

26.

Math 17.05

C

D

B

A

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27. ∫ 1/xInx dx =

In x + c

x + c

In In x + c

In In In x + c

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28. In 2 ∫ 2ˣ dx =

1/2ˣ In 2 + c

2ˣ/In 2 + c

In 2/2ˣ + c

2ˣ + c

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

-2

1

0

2

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

f(x) + f(sx)

y + s (x + sx)

f(x), f(sx)

f(x) + dy

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31. ∫ eˣ [sinh⁻¹ x + 1/√1+x²] dx = ?

eˣ sinh⁻¹ x + c

eˣ cos⁻¹ x + c

eˣ tan⁻¹x + c

eˣ cos h⁻¹ x

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32. ∫ dX/X² – 9 = ?

1/6 In x–3/x+3 + c

None of these

1/6 In x+3/x–3 + c

1/9 Tan ⁻¹(x/9) + c

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33. In a ∫ aˣ dx =

in a/aˣ + c

aˣ + c

aˣ/in a + c

1/aˣin a + c

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34. ∫(∫ 1/x sec² x/Tanx)dx

In (x cotx)

Inx – Tanx + c

In(x Tanx) + c

Inx – cot x + c

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35. ∫ 2x+5/x²+5x dx

In|2x+5|+c

x²+5x

In|x²+5x| + c

3x + 5

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36.

Math 17.02

D

B

A

C

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37. ∫ cos xdx/sin x In sin x = ?

Incosx + c

In(In cos x) c

In(In sinx) + c

In sinx + c

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38.

Math 17.01

A

B

C

D

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39. ∫ –2x/√4 – x² dx

8 – 2x² + c

2√4–x² + c

2√x²–4 + c

2√x²+4

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40.

Math 17.06

D

C

A

B

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41. ∫ dx/√a² – x² =

sinh⁻¹(x/a) + c

sin⁻¹ x + c

cosh⁻¹(x/a) + c

sin⁻¹(x/a) + c

Loading...

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

Anti – derivatives

Derivative of f(x)

Derivatives of Ø

None of these

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43. ∫ - 3cosec² 3xdx =

cot 3x + c

tan 3x + c

-cos 3x + c

-cot3x + c

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

Zero

49

45

40

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45. ∫sin xdx =

-cos x + c

Cotx + c

Cos x + c

Tanx + c

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46. ∫(eˣ - sin2x/cos²x) dx =

In(ex cos²x) + c

In(xsin²x) + c

In(xcos²x) + c

In(xsinx) + c

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

2 In cotx + c

In cotx + c

In tanx + c

2 In tanx + c

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48. The integration is the reverse process of

Sublimation

Classification

Differentiation

Tabulation

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49. ∫ a/xⁿ dx ?

axⁿ⁻¹/1 – n

axⁿ⁺¹/n+1 + c

axⁿ⁻¹(n – 1) + c

(ax)ⁿ⁺¹

Loading...

50. ∫ 1/1+x² dx =

cot⁻¹ x + c

cos⁻¹ x + c

-cot⁻¹ x + c

sin⁻¹ x + c

Loading...

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Maan AliLast Updated: October 15, 2025

Maan Ali

Hey there! I'm Maan Ali, your online test prep pal. Join me in the adventure of acing exams with ease. I'll share tricks, practice tests, and all you need to rock your studies. Let's make learning fun and success a sure thing!

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