Punjab 12th Class Math Chapter 3 Integration Mcqs Test Online

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Question 1 of 20

Math

1. e ͯ[lnx + 1/x]dx = ________

1.lnx – e ͯ+ c

2.e ͯ lnx + c

3.e ͯ/x + c

4.In x + e ͯ+ c

Question 1 of 20

Question 2 of 20

2. ∫x Cos x dx = _________

1.x Sin x + Cos x + c

2.x Sin x – Cosx + c

3.x Cos x + Sin x + c

4.x Sin x + c

Question 2 of 20

Question 3 of 20

3. ∫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 3 of 20

Question 4 of 20

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

1.y = Cos (e ͯ + c)

2.y = Tan (e ͯ + c)

3.y = Sin (e ͯ + c)

4.y = Cot (e ͯ + c)

Question 4 of 20

Question 5 of 20

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

1.Y = e⁻ ͯ

2.Y = ce ͯ

3.Y = ce⁻ ͯ

4.Y = e ͯ

Question 5 of 20

Question 6 of 20

6. ∫ 1/ax + b dx = __________

1.(ax + b)/b+c

2.1/b ln|ax + b| + c

3.1/b In |ax – b| + c

4.1/a ln|ax + b| + c

Question 6 of 20

Question 7 of 20

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

1.sec²y

2.secy + c

3.tany

4.sec y tan y

Question 7 of 20

Question 8 of 20

8. d/dx & ∫ ……… dx are:

1.Same operations

2.None of these

3.No relation between these two

4.Inverse operations

Question 8 of 20

Question 9 of 20

9. ∫ 1/ax + b dx equals

1.In (ax + b) + c

2.loga (ax + b) + c

3.a In(ax + b) + c

4.1/a In(ax + b) + c

Question 9 of 20

Question 10 of 20

10. ∫ 2 ͯ(1n2) dx =

1.2 ͯ/1n2 + c

2.1n2/2 ͯ + c

3.1/2 ͯ1n2

4.2 ͯ + c

Question 10 of 20

Question 11 of 20

11. ∫ Cosec²(ax + b) d

1.1/a cot (ax + b) + c

2.-1/a tan(ax + b) + c

3.a tan (ax + b) + c

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

Question 11 of 20

Question 12 of 20

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

1.B

2.C

3.D

4.A

Question 12 of 20

Question 13 of 20

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

1.(ax + b)ⁿ⁺¹/a + c

2.(ax + b)ⁿ⁺¹/a(n+1)+c

3.(ax + b)ⁿ⁺¹/a(n + 1) + c

4.(ax + b)ⁿ⁺¹+c

Question 13 of 20

Question 14 of 20

14. 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 14 of 20

Question 15 of 20

15. ∫ dx/a² – x² dx = __________

1.Sin⁻¹ x/a + c

2.Sin⁻¹ a/x + c

3. Sin⁻¹ x + c

4.Cos⁻¹ x/c + c

Question 15 of 20

Question 16 of 20

16. 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.Area

3.Function

4.Integral

Question 16 of 20

Question 17 of 20

17. The anti derivative of zero is

1.1

2.constant

3.0

4.x

Question 17 of 20

Question 18 of 20

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

1.tan²y + c

2.tany + c

3.cosec²y + c

4.cosecy + c

Question 18 of 20

Question 19 of 20

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

1.x = a cot θ

2.x = a tan θ

3.x = a cosec θ

4.x = a sin θ

Question 19 of 20

Question 20 of 20

20. ∫lnx dx = ________

1.xln x + c

2.ln x + x + c

3.x lnx – x + c

4.x lnx + x + c

Question 20 of 20

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