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.Integral

2.Area

3.None of these

4.Function

Question 1 of 20

Question 2 of 20

2. e ͯ[lnx + 1/x]dx = ________

1.e ͯ lnx + c

2.In x + e ͯ+ c

3.e ͯ/x + c

4.lnx – e ͯ+ c

Question 2 of 20

Question 3 of 20

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

1.(ax + b)ⁿ⁺¹/a(n + 1) + c

2.(ax + b)ⁿ⁺¹/a(n+1)+c

3.(ax + b)ⁿ⁺¹+c

4.(ax + b)ⁿ⁺¹/a + c

Question 3 of 20

Question 4 of 20

4. ∫ 1/ax + b dx = __________

1.1/a ln|ax + b| + c

2.1/b ln|ax + b| + c

3.(ax + b)/b+c

4.1/b In |ax – b| + c

Question 4 of 20

Question 5 of 20

5. The anti derivative of zero is

1.x

2.0

3.1

4.constant

Question 5 of 20

Question 6 of 20

6. ∫ 2 ͯ(1n2) dx =

1.1/2 ͯ1n2

2.1n2/2 ͯ + c

3.2 ͯ/1n2 + c

4.2 ͯ + c

Question 6 of 20

Question 7 of 20

7. d/dx & ∫ ……… dx are:

1.Inverse operations

2.No relation between these two

3.None of these

4.Same operations

Question 7 of 20

Question 8 of 20

8. ∫lnx dx = ________

1.x lnx + x + c

2.ln x + x + c

3.xln x + c

4.x lnx – x + c

Question 8 of 20

Question 9 of 20

9. ∫ dx/a² – x² dx = __________

1. Sin⁻¹ x + c

2.Cos⁻¹ x/c + c

3.Sin⁻¹ x/a + c

4.Sin⁻¹ a/x + c

Question 9 of 20

Question 10 of 20

10. 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

1.3t² + c

2.3t² + c

3.t³ + c

4.T³ + c

Question 10 of 20

Question 11 of 20

11. ∫ 1/ax + b dx equals

1.In (ax + b) + c

2.a In(ax + b) + c

3.1/a In(ax + b) + c

4.loga (ax + b) + c

Question 11 of 20

Question 12 of 20

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

1.x = a sin θ

2.x = a cosec θ

3.x = a tan θ

4.x = a cot θ

Question 12 of 20

Question 13 of 20

13. ∫ Cosec²(ax + b) d

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

2.1/a cot (ax + b) + c

3.a tan (ax + b) + c

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

Question 13 of 20

Question 14 of 20

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

1.cosecy + c

2.tany + c

3.cosec²y + c

4.tan²y + c

Question 14 of 20

Question 15 of 20

15. ∫x Sin x dx = __________

1.x Sin x – Sin x + c

2.Sin x – x Cos x + c

3.x Sin x – Cos x + c

4.x Sin x + x Cosx + c

Question 15 of 20

Question 16 of 20

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

1.Y = e⁻ ͯ

2.Y = ce ͯ

3.Y = e ͯ

4.Y = ce⁻ ͯ

Question 16 of 20

Question 17 of 20

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

1.y = Tan (e ͯ + c)

2.y = Cot (e ͯ + c)

3.y = Sin (e ͯ + c)

4.y = Cos (e ͯ + c)

Question 17 of 20

Question 18 of 20

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

1.sec²y

2.tany

3.secy + c

4.sec y tan y

Question 18 of 20

Question 19 of 20

19. ∫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 19 of 20

Question 20 of 20

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

1.A

2.C

3.D

4.B

Question 20 of 20

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