Punjab 12th Class Math Chapter 3 Integration Mcqs Test Online

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Question 1 of 20

Math

1. ∫x Cos x dx = _________

1.x Sin x – Cosx + c

2.x Sin x + c

3.x Sin x + Cos x + c

4.x Cos x + Sin x + c

Question 1 of 20

Question 2 of 20

2. ∫x Sin x dx = __________

1.Sin x – x Cos x + c

2.x Sin x + x Cosx + c

3.x Sin x – Cos x + c

4.x Sin x – Sin x + c

Question 2 of 20

Question 3 of 20

3. ∫ 1/ax + b dx equals

1.In (ax + b) + c

2.a In(ax + b) + c

3.loga (ax + b) + c

4.1/a In(ax + b) + c

Question 3 of 20

Question 4 of 20

4. 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.t³ + c

3.T³ + c

4.3t² + c

Question 4 of 20

Question 5 of 20

5. e ͯ[lnx + 1/x]dx = ________

1.e ͯ/x + c

2.In x + e ͯ+ c

3.e ͯ lnx + c

4.lnx – e ͯ+ c

Question 5 of 20

Question 6 of 20

6. ∫ dx/a² – x² dx = __________

1. Sin⁻¹ x + c

2.Sin⁻¹ x/a + c

3.Cos⁻¹ x/c + c

4.Sin⁻¹ a/x + c

Question 6 of 20

Question 7 of 20

7. ∫lnx dx = ________

1.xln x + c

2.x lnx + x + c

3.x lnx – x + c

4.ln x + x + c

Question 7 of 20

Question 8 of 20

8. The anti derivative of zero is

1.constant

2.1

3.0

4.x

Question 8 of 20

Question 9 of 20

9. ∫ 1/ax + b dx = __________

1.1/b In |ax – b| + c

2.1/a ln|ax + b| + c

3.1/b ln|ax + b| + c

4.(ax + b)/b+c

Question 9 of 20

Question 10 of 20

10. 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.Function

3.Area

4.None of these

Question 10 of 20

Question 11 of 20

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

1.x = a sin θ

2.x = a cosec θ

3.x = a cot θ

4.x = a tan θ

Question 11 of 20

Question 12 of 20

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

1.Y = ce ͯ

2.Y = e⁻ ͯ

3.Y = ce⁻ ͯ

4.Y = e ͯ

Question 12 of 20

Question 13 of 20

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

1.tany + c

2.tan²y + c

3.cosecy + c

4.cosec²y + c

Question 13 of 20

Question 14 of 20

14. ∫ 2 ͯ(1n2) dx =

1.2 ͯ + c

2.1/2 ͯ1n2

3.2 ͯ/1n2 + c

4.1n2/2 ͯ + c

Question 14 of 20

Question 15 of 20

15. ∫ Cosec²(ax + b) d

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

2.a tan (ax + b) + c

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

4.1/a cot (ax + b) + c

Question 15 of 20

Question 16 of 20

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

1.y = Cot (e ͯ + c)

2.y = Sin (e ͯ + c)

3.y = Cos (e ͯ + c)

4.y = Tan (e ͯ + c)

Question 16 of 20

Question 17 of 20

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

1.(ax + b)ⁿ⁺¹/a(n+1)+c

2.(ax + b)ⁿ⁺¹+c

3.(ax + b)ⁿ⁺¹/a(n + 1) + c

4.(ax + b)ⁿ⁺¹/a + c

Question 17 of 20

Question 18 of 20

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

1.tany

2.sec y tan y

3.secy + c

4.sec²y

Question 18 of 20

Question 19 of 20

19. d/dx & ∫ ……… dx are:

1.Inverse operations

2.None of these

3.No relation between these two

4.Same operations

Question 19 of 20

Question 20 of 20

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

$Math 3.1$ $Math 3.2$

1.B

2.C

3.A

4.D

Question 20 of 20

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