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Home/ECAT/ECAT Mathematics Integration Online Test

ECAT Mathematics Integration Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Integration

ECAT Math Integration Chapter Online Test

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

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Page 1 of 2

1. ∫ 1/1+x² dx =

tan⁻¹ x + c

sin⁻¹ x + c

cos⁻¹ x + c

cot⁻¹ x + c

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

45

49

Zero

40

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3. ∫ (Tan⁴ x + Tan² x) dx = ?

Tan⁴ x/4

Tan³x/3

None of these

Tan⁵ x/5

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

None of these

Anti – derivatives

Derivatives of Ø

Derivative of f(x)

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

f(x) + dy

f(x), f(sx)

y + s (x + sx)

f(x) + f(sx)

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6. ∫(eˣ + cosc) = dx

ex – sin x + c

ex + sinx + c

Sinx + c

-sinx + c

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7. ∫ dX/X² – 9 = ?

1/6 In x+3/x–3 + c

1/6 In x–3/x+3 + c

None of these

1/9 Tan ⁻¹(x/9) + c

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8. ∫ dx/xsin²(ln x) = ?

-tan(lnx)

Cot(lnx)

-cot(lnx)

Tan (lnx)

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9. ∫ –2x/√4 – x² dx

2√x²–4 + c

8 – 2x² + c

2√x²+4

2√4–x² + c

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10. ∫(√x – 1/√x)² dx =

½ x² – 2x + In x + c

x² – x + In x + c

½ x² + In x + c

½ x² – 2x + c

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11. ∫ sin⁻¹ (cos)dx = ?

πx/2

πx/2 – x²/2

πx + x²/2

x²/2

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12.

C

D

B

A

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13. ∫ -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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14. ∫(∫ 1/x sec² x/Tanx)dx

In (x cotx)

Inx – Tanx + c

In(x Tanx) + c

Inx – cot x + c

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15.

C

B

D

A

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16. Suitable substitution to integrate √x²–a² is

x = a tan Ø

x = a sin Ø

x = a cot Ø

x = a sec Ø

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17. ∫ 2x+5/x²+5x dx

In|2x+5|+c

x²+5x

In|x²+5x| + c

3x + 5

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

0

-2

2

1

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19. ∫ dx/√a² – x² =

sin⁻¹(x/a) + c

sinh⁻¹(x/a) + c

sin⁻¹ x + c

cosh⁻¹(x/a) + c

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20. ∫ cos xdx/sin x In sin x = ?

In sinx + c

Incosx + c

In(In cos x) c

In(In sinx) + c

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21. 6/(x³ – 3x²)⁶ ∫ (x³ – 3x²)⁵ (3x² – 6x) dx =

(x³ – 3x²)⁴/4 + c

c

(x³ – 3x²)⁶/6 + c

(x³ – 3x²)⁶ + c

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22. ∫ eˣ [sinh⁻¹ x + 1/√1+x²] dx = ?

eˣ tan⁻¹x + c

eˣ cos⁻¹ x + c

eˣ sinh⁻¹ x + c

eˣ cos h⁻¹ x

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

y = cotx + c

y = sec⁻¹ x

y = sin⁻¹ x + c

y = tan⁻¹ x + c

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24.

A

C

D

B

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25.

B

A

D

C

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26. ∫ cot xdx =

In sinx + c

In cosecx + c

In cotx + c

In secx + c

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27.

B

C

A

D

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

2 In cotx + c

In tanx + c

2 In tanx + c

In cotx + c

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29. ∫ [eˣ - sin2x/cos²x]dx = ?

In(x sinx) + c

In(x sin²x) + c

In(eˣ cos² x) + c

In(x cos²x) + c

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30. ∫ a/xⁿ dx ?

(ax)ⁿ⁺¹

axⁿ⁻¹/1 – n

axⁿ⁻¹(n – 1) + c

axⁿ⁺¹/n+1 + c

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31. In 2 ∫ 2ˣ dx =

2ˣ/In 2 + c

2ˣ + c

1/2ˣ In 2 + c

In 2/2ˣ + c

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32. ∫ 1/xInx dx =

x + c

In x + c

In In In x + c

In In x + c

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33. The integration is the reverse process of

Classification

Sublimation

Tabulation

Differentiation

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34. ∫ Tanxdx/In sec x = ?

In(In sec x) + c

In(In cosx) + c

In (In tan x) + c

In (In cot x) + c

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35. ∫(eˣ - sin2x/cos²x) dx =

In(xcos²x) + c

In(xsinx) + c

In(xsin²x) + c

In(ex cos²x) + c

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36. ∫ 6(x³ – 3x²)⁵ (3x² – 6x)dx = ?

(x³ – 3x²)⁴/4 + c

(x³ – 3x²)⁶/6 + c

None of these

(x³ – 3x²)⁶ + c

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

[f(x)]ⁿ⁻¹/n +c

[f(x)]ⁿ⁺¹/n + 1 +c

[f(x)]ⁿ⁻¹/n – 1 +c

n[f(x)]ⁿ⁻¹ +c

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38. ∫ 1/1+x² dx =

cos⁻¹ x + c

sin⁻¹ x + c

cot⁻¹ x + c

-cot⁻¹ x + c

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

Cos x = cos y

Cos y – cos x = c

Sin x = sin y

Sin x + sin y = c

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40. In a ∫ aˣ dx =

1/aˣin a + c

in a/aˣ + c

aˣ/in a + c

aˣ + c

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41. ∫sin xdx =

Tanx + c

-cos x + c

Cotx + c

Cos x + c

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42.

C

B

A

D

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43. ∫(1/x + cosec²x/cotx) dx =

In(xtanx)+c

In(xcotx)+c

Inx–cotx+c

Inx+tanx+c

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44. ∫ - 2cosec² 2xdx =

Cos2x + c

Tan2x + c

-cos2x + c

Cot2x + c

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

64/3

32/3

32

64

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46. ∫ dx/√a² – x² = ?

Sin⁻¹ x/a + c

A sin⁻¹ x/a

1/a sin⁻¹ x/a

1/a Tan⁻¹ x/a

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47. ∫ - 3cosec² 3xdx =

-cot3x + c

cot 3x + c

tan 3x + c

-cos 3x + c

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48. ∫ d/dx (x² + 3x) dx =

2x + 3

2x + 3 + c

x³/3 + 3x²/2 + c

x² + 3x + c

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49. ∫ 2x – 1/x²–x+1 dx =

In(x² – x + 1) + c

(2x – 1) + c

0

In(2x – 1) + c

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50. ∫ dx/x² – a² =

½ In x–a/x+a + c

½ In a+x/a–x + c

½ In x+a/x–a + c

½ tan In (x/a) + c

Loading...

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Danial MalikLast Updated: April 18, 2025

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