Punjab 12th Class Math Chapter 3 Integration Mcqs Test Online

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Question 1 of 20

Math

1. ∫(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+c

4.(ax + b)ⁿ⁺¹/a(n+1)+c

Question 1 of 20

Question 2 of 20

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

$Math 3.1$ $Math 3.2$

1.D

2.B

3.C

4.A

Question 2 of 20

Question 3 of 20

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

1.y = Cot (e ͯ + c)

2.y = Cos (e ͯ + c)

3.y = Sin (e ͯ + c)

4.y = Tan (e ͯ + c)

Question 3 of 20

Question 4 of 20

4. ∫ 2 ͯ(1n2) dx =

1.2 ͯ/1n2 + c

2.2 ͯ + c

3.1/2 ͯ1n2

4.1n2/2 ͯ + c

Question 4 of 20

Question 5 of 20

5. e ͯ[lnx + 1/x]dx = ________

1.lnx – e ͯ+ c

2.e ͯ/x + c

3.e ͯ lnx + c

4.In x + e ͯ+ c

Question 5 of 20

Question 6 of 20

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

1.Y = e ͯ

2.Y = e⁻ ͯ

3.Y = ce⁻ ͯ

4.Y = ce ͯ

Question 6 of 20

Question 7 of 20

7. 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

3.3t² + c

4.T³ + c

Question 7 of 20

Question 8 of 20

8. ∫x Sin x dx = __________

1.x Sin x – Sin x + c

2.x Sin x – Cos x + c

3.x Sin x + x Cosx + c

4.Sin x – x Cos x + c

Question 8 of 20

Question 9 of 20

9. 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 9 of 20

Question 10 of 20

10. ∫ 1/ax + b dx equals

1.loga (ax + b) + c

2.In (ax + b) + c

3.1/a In(ax + b) + c

4.a In(ax + b) + c

Question 10 of 20

Question 11 of 20

11. ∫lnx dx = ________

1.x lnx + x + c

2.ln x + x + c

3.xln x + c

4.x lnx – x + 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 cot θ

3.x = a tan θ

4.x = a cosec θ

Question 12 of 20

Question 13 of 20

13. ∫ dx/a² – x² dx = __________

1.Sin⁻¹ a/x + c

2.Sin⁻¹ x/a + c

3. Sin⁻¹ x + c

4.Cos⁻¹ x/c + c

Question 13 of 20

Question 14 of 20

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

1.cosec²y + c

2.tany + c

3.tan²y + c

4.cosecy + c

Question 14 of 20

Question 15 of 20

15. 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.Function

2.None of these

3.Area

4.Integral

Question 15 of 20

Question 16 of 20

16. The anti derivative of zero is

1.constant

2.x

3.0

4.1

Question 16 of 20

Question 17 of 20

17. ∫x Cos x dx = _________

1.x Sin x + Cos x + c

2.x Cos x + Sin x + c

3.x Sin x + c

4.x Sin x – Cosx + c

Question 17 of 20

Question 18 of 20

18. d/dx & ∫ ……… dx are:

1.None of these

2.No relation between these two

3.Inverse operations

4.Same operations

Question 18 of 20

Question 19 of 20

19. ∫ Cosec²(ax + b) d

1.1/a cot (ax + b) + c

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

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

4.a tan (ax + b) + c

Question 19 of 20

Question 20 of 20

20. ∫ 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 20 of 20

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