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Unit 5: Integration II - Practice Quiz

MTH110 — Remedial Mathematics 60 Questions
0 Correct 0 Wrong 60 Left
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1 The formula for integration by parts is ?

integration by parts Easy
A.
B.
C.
D.

2 In the ILATE rule for choosing the first function in integration by parts, what does the letter 'L' stand for?

integration by parts Easy
A. Linear function
B. Limit function
C. Logarithmic function
D. Laplace function

3 Using integration by parts, ?

integration by parts Easy
A.
B.
C.
D.

4 When evaluating by parts, which function should be chosen as according to ILATE?

integration by parts Easy
A.
B.
C.
D.

5 The value of is:

integration by parts Easy
A.
B.
C.
D.

6 The Fundamental Theorem of Calculus states that ? where .

definite integral Easy
A.
B.
C.
D.

7 Evaluate .

definite integral Easy
A.
B.
C.
D.

8 Evaluate .

definite integral Easy
A.
B.
C.
D.

9 A definite integral gives a result that is:

definite integral Easy
A. Always zero
B. A function of
C. A function of
D. A number (constant)

10 Evaluate .

definite integral Easy
A.
B.
C.
D.

11 Evaluate .

definite integral Easy
A.
B.
C.
D.

12 In the definition of the definite integral as the limit of a sum, of a sum where ?

definite integral as the limit of a sum Easy
A.
B.
C.
D.

13 The definite integral as the limit of a sum is written as . This sum is called a:

definite integral as the limit of a sum Easy
A. Riemann sum
B. Geometric sum
C. Binomial sum
D. Harmonic sum

14 As the number of subintervals increases to infinity in the limit of a sum, the width of each subinterval approaches:

definite integral as the limit of a sum Easy
A.
B.
C.
D.

15 Geometrically, the definite integral (with ) represents:

definite integral as the limit of a sum Easy
A. The length of the curve from to
B. The area under the curve between and
C. The maximum value of
D. The slope of the curve at

16 What is the value of ?

some properties of definite integrals Easy
A.
B.
C.
D.

17 Which property correctly relates the swapping of limits in a definite integral?

some properties of definite integrals Easy
A.
B.
C.
D.

18 The property holds when:

some properties of definite integrals Easy
A. always
B.
C. only
D. only

19 If is an odd function, then ?

some properties of definite integrals Easy
A.
B.
C.
D.

20 If is an even function, then ?

some properties of definite integrals Easy
A.
B.
C.
D.

21 Evaluate .

integration by parts Medium
A.
B.
C.
D.

22 Evaluate .

integration by parts Medium
A.
B.
C.
D.

23 Evaluate .

integration by parts Medium
A.
B.
C.
D.

24 Evaluate .

integration by parts Medium
A.
B.
C.
D.

25 Using the ILATE rule, which function should be chosen as the first function () in ?

integration by parts Medium
A.
B.
C.
D.

26 Evaluate .

integration by parts Medium
A.
B.
C.
D.

27 Evaluate .

definite integral Medium
A.
B.
C.
D.

28 Evaluate .

definite integral Medium
A.
B.
C.
D.

29 Evaluate .

definite integral Medium
A.
B.
C.
D.

30 Evaluate .

definite integral Medium
A.
B.
C.
D.

31 Evaluate .

definite integral Medium
A.
B.
C.
D.

32 Evaluate .

definite integral Medium
A.
B.
C.
D.

33 As the limit of a sum, equals which of the following (with )?

definite integral as the limit of a sum Medium
A.
B.
C.
D.

34 Using the limit of a sum, evaluate .

definite integral as the limit of a sum Medium
A.
B.
C.
D.

35 In evaluating as a limit of a sum, what is the value of ?

definite integral as the limit of a sum Medium
A.
B.
C.
D.

36 Using the limit of a sum, evaluate .

definite integral as the limit of a sum Medium
A.
B.
C.
D.

37 The value of is:

some properties of definite integrals Medium
A.
B.
C.
D.

38 Using the property for even , evaluate .

some properties of definite integrals Medium
A.
B.
C.
D.

39 Using , the integral equals:

some properties of definite integrals Medium
A.
B.
C.
D.

40 The value of is:

some properties of definite integrals Medium
A.
B.
C.
D.

41 Evaluate .

integration by parts Hard
A.
B.
C.
D.

42 Evaluate .

integration by parts Hard
A.
B.
C.
D.

43 Evaluate .

integration by parts Hard
A.
B.
C.
D.

44 Evaluate .

integration by parts Hard
A.
B.
C.
D.

45 Evaluate .

integration by parts Hard
A.
B.
C.
D.

46 Evaluate .

integration by parts Hard
A.
B.
C.
D.

47 Evaluate .

definite integral Hard
A.
B.
C.
D.

48 Evaluate .

definite integral Hard
A.
B.
C.
D.

49 Evaluate .

definite integral Hard
A.
B.
C.
D.

50 Evaluate .

definite integral Hard
A.
B.
C.
D.

51 Using the limit of a sum, equals:

definite integral as the limit of a sum Hard
A.
B.
C.
D.

52 Evaluate .

definite integral as the limit of a sum Hard
A.
B.
C.
D.

53 Evaluate .

definite integral as the limit of a sum Hard
A.
B.
C.
D.

54 Evaluate .

definite integral as the limit of a sum Hard
A.
B.
C.
D.

55 Using the limit of a sum, equals:

definite integral as the limit of a sum Hard
A.
B.
C.
D.

56 Evaluate .

some properties of definite integrals Hard
A.
B.
C.
D.

57 Evaluate .

some properties of definite integrals Hard
A.
B.
C.
D.

58 Evaluate .

some properties of definite integrals Hard
A.
B.
C.
D.

59 Evaluate .

some properties of definite integrals Hard
A.
B.
C.
D.

60 Evaluate .

some properties of definite integrals Hard
A.
B.
C.
D.
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