Punjab 12th Class Math Chapter 3 Integration Mcqs Test Online

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Question 1 of 20

Math

1. The definite integral ᵇ∫f(x) dx represents the __________ above the x-axis and under the curve y = f(x) from x = a to x = b

1.None of these

2.Integral

3.Function

4.Area

Question 1 of 20

Question 2 of 20

2. The anti derivative of the function f(y) = secy tan y is

1.secy + c

2.sec y tan y

3.sec²y

4.tany

Question 2 of 20

Question 3 of 20

3. d/dx & ∫ ……… dx are:

1.None of these

2.No relation between these two

3.Same operations

4.Inverse operations

Question 3 of 20

Question 4 of 20

4. ∫ 1/ax + b dx equals

1.1/a In(ax + b) + c

2.In (ax + b) + c

3.loga (ax + b) + c

4.a In(ax + b) + c

Question 4 of 20

Question 5 of 20

5. ∫ dx/a² – x² dx = __________

1.Sin⁻¹ a/x + c

2. Sin⁻¹ x + c

3.Cos⁻¹ x/c + c

4.Sin⁻¹ x/a + c

Question 5 of 20

Question 6 of 20

6. If the velocity of a particle moving in a straight line is given by v = 3t² then the distance traveled by it in the first T seconds is

1.T³ + c

2.t³ + c

3.3t² + c

4.3t² + c

Question 6 of 20

Question 7 of 20

7. The shaded area in the figure can be represented by

1.B

2.D

3.A

4.C

Question 7 of 20

Question 8 of 20

8. ∫ Cosec²(ax + b) d

1.a tan (ax + b) + c

2.1/a cot (ax + b) + c

3.-1/a Cot (ax + b) + c

4.-1/a tan(ax + b) + c

Question 8 of 20

Question 9 of 20

9. The solution of dy/dx = -y is __________

1.Y = e⁻ ͯ

2.Y = e ͯ

3.Y = ce ͯ

4.Y = ce⁻ ͯ

Question 9 of 20

Question 10 of 20

10. The solution of dy/y² + 1 = e ͯ dx is

1.y = Sin (e ͯ + c)

2.y = Cot (e ͯ + c)

3.y = Cos (e ͯ + c)

4.y = Tan (e ͯ + c)

Question 10 of 20

Question 11 of 20

11. e ͯ[lnx + 1/x]dx = ________

1.e ͯ/x + c

2.In x + e ͯ+ c

3.e ͯ lnx + c

4.lnx – e ͯ+ c

Question 11 of 20

Question 12 of 20

12. Substitution for the integrals involving the expression √a² - x can be:

1.x = a tan θ

2.x = a sin θ

3.x = a cosec θ

4.x = a cot θ

Question 12 of 20

Question 13 of 20

13. ∫ 2 ͯ(1n2) dx =

1.1n2/2 ͯ + c

2.2 ͯ + c

3.2 ͯ/1n2 + c

4.1/2 ͯ1n2

Question 13 of 20

Question 14 of 20

14. ∫(ax + b)ⁿ dx = __________, if n≠ -1 then

1.(ax + b)ⁿ⁺¹+c

2.(ax + b)ⁿ⁺¹/a + c

3.(ax + b)ⁿ⁺¹/a(n+1)+c

4.(ax + b)ⁿ⁺¹/a(n + 1) + c

Question 14 of 20

Question 15 of 20

15. The anti derivative of the function f(y) = tan²y cosec²y is

1.cosecy + c

2.cosec²y + c

3.tan²y + c

4.tany + c

Question 15 of 20

Question 16 of 20

16. ∫ 1/ax + b dx = __________

1.1/b In |ax – b| + c

2.(ax + b)/b+c

3.1/b ln|ax + b| + c

4.1/a ln|ax + b| + c

Question 16 of 20

Question 17 of 20

17. ∫x Cos x dx = _________

1.x Cos x + Sin x + c

2.x Sin x + Cos x + c

3.x Sin x + c

4.x Sin x – Cosx + c

Question 17 of 20

Question 18 of 20

18. The anti derivative of zero is

1.1

2.x

3.constant

4.0

Question 18 of 20

Question 19 of 20

19. ∫x Sin x dx = __________

1.x Sin x – Sin x + c

2.x Sin x + x Cosx + c

3.x Sin x – Cos x + c

4.Sin x – x Cos x + c

Question 19 of 20

Question 20 of 20

20. ∫lnx dx = ________

1.ln x + x + c

2.x lnx – x + c

3.xln x + c

4.x lnx + x + c

Question 20 of 20

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