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Calculus Problem Set

1. The document contains 50 multiple choice questions related to integrals. 2. The questions cover a range of integral evaluation techniques including substitution, integration by parts, and finding antiderivatives of standard functions. 3. Many questions ask the reader to identify the correct integral expression or evaluate specific integrals.

Uploaded by

Sanjib Saha
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
124 views9 pages

Calculus Problem Set

1. The document contains 50 multiple choice questions related to integrals. 2. The questions cover a range of integral evaluation techniques including substitution, integration by parts, and finding antiderivatives of standard functions. 3. Many questions ask the reader to identify the correct integral expression or evaluate specific integrals.

Uploaded by

Sanjib Saha
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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1.

Given ∫ 2x dx = f(x) + C, then f(x) is

2.

(a) sin² x – cos² x + C


(b) -1
(c) tan x + cot x + C
(d) tan x – cot x + C
3.

(a) 2(sin x + x cos θ) + C


(b) 2(sin x – x cos θ) + C
(c) 2(sin x + 2x cos θ) + C
(d) 2(sin x – 2x cos θ) + C
4. ∫cot²x dx equals to
(a) cot x – x + C
(b) cot x + x + C
(c) -cot x + x + C
(d) -cot x – x + C
5.

(a) log |sin x + cos x|


(b) x
(c) log |x|
(d) -x

6. If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is


(a) 7
(b) -4
(c) 3
(d) −14
7. The value of  for which

(a) 1
(b) loge4
(c) loe4 e
(d) 4
8.

9.

then value of a is equal to


(a) 3
(b) 6
(c) 9
(d) 1
10.
11.

12.

(a) I1 > I2
(b) I2 > I1
(c) I1 = I2
(d) I1 > 2I2
a

13. If a is such that ∫ xdx ≤ a + 4, then


0

(a) 0 ≤ a ≤ 4
(b) -2 ≤ a ≤ 0
(c) a ≤ -2 or a ≤ 4
(d) -2 ≤ a ≤ 4
d
14. If  dx  (f(x) )= g(x), then antiderivative of g(x) is ________ .

15. Derivative of a function is unique but a function can have infinite


antiderivatives. State true or false.
16.

17. Find ∫(ax + b)3dx


18. If ∫(ax + b)² dx = f(x) + C, find f(x)

d
19. We have  dx (3x² + sin x – ex) = 6x + cos x -ex. Represent the expression in
the form of anti derivative.
20.
21.

22. Evaluate ∫ (sin x + cos x)² dx


23.

24.

25. Find ∫(ex log a + ea log x + ea log a)dx


1
26. Evaluate ∫e 2 logxdx.
27.

(a) 3x + x3 + C


(b) log |3x + x3| + C
(c) 3x²+ 3x loge 3 +C
(d) log |3x² + 3x loge 3| + C
28.

e√x
29.∫ dx=?
√x
30.

31. Find ∫ sec² (7 – x)dx


sin √ x
32. Find ∫ dx
√x
33. Find ∫2x sin(x² + 1) dx
34.

35.
36.

37.

38.

39.

40.

41.

42.

43.

44. Evaluate ∫ sec4 x tan x dx


45.

46.

47. Find ∫ cot x . log(sin x) dx


48.

49. Find ∫(ex + 3x)² (ex + 3)dx


50.
51.

52. Find ∫ (cosx – sinx)² dx


53. Evaluate ∫1+sinx4−−−−−−−√dx

54.

55.

56.

57.

58.

59.

60. ∫ ex sec x(1 + tan x)dx = ________ + C.


4 4 2

61. If ∫ f ( x) dx =4 and ∫ { 3−f ( x ) } dx = 7, then the value of ∫ f (x)is


−1 2 −1

62.

63.

64.

65.
a 3

66. If ∫ 3 x dx = 8 write the value of a. 67. Evaluate. ∫ 3 dx


2 x

0 2

68.

2a a

69.∫ f (x )dx = 2 ∫ f ( x ) dx if f(2a -x)= f(x). State true or false.


0 0

70.

then value of a is ________ .


71.

72. ∫ |1−x|dx is equal to ________ .


−1

73.

is equal to 0.State true or false.

74. The value of ∫|cos x−1|dx  | is 2. State true or false.


0

75. The value of ∫ sin x cos xdx dx is ________ .


3 2

−π

76.

77.

78.
79.

80. Evaluate ∫ x| x| ⅆx
−1
2π

81. Evaluate ∫ cos x dx


5

82.

83. Evaluate ∫ [2 x ]dx


0
4

84. Evaluate ∫ f ( x ) x dx , where


1

85.

86. Evaluate ∫ ( sin


−93 295
+ x )dx
−π

87.

88.

89.

90. Find the value of ∫ logx . dx


1

91. Evaluate  ∫ x (1− x).dx


0
92.

93. Evaluate  ∫ x (1−x ) dx


2 n

94.

95. Evaluate  ∫|cos x| ⅆx


0

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