# Maths MCQs for Class 12 with Answers Chapter 7 Integrals

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 7 Integrals. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Integrals MCQs Pdf with Answers to know their preparation level.

## Integrals Class 12 Maths MCQs Pdf

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

Explaination:

2.

(a) sin² x – cos² x + C
(b) -1
(c) tan x + cot x + C
(d) tan x – cot x + C

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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

Explaination:

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

Explaination: (d), ∫ (cosec²x -1)dx = -cot x – x + C

5.

(a) log |sin x + cos x|
(b) x
(c) log |x|
(d) -x

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6. If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is
(a) 7
(b) -4
(c) 3
(d) $$-\frac{1}{4}$$

Explaination:
(d), ∫sec²(7 – 4x)dx = $$\frac{\tan (7-4 x)}{-4}$$ + C = –$$\frac{1}{4}$$ tan (7 – 4x) + C.

7. The value of X for which

(a) 1
(b) loge4
(c) loe4 e
(d) 4

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8.

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9.

then value of a is equal to
(a) 3
(b) 6
(c) 9
(d) 1

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10.

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11.

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12.

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

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13. If a is such that $$\int_{0}^{a} x d x$$ ≤ a + 4, then
(a) 0 ≤ a ≤ 4
(b) -2 ≤ a ≤ 0
(c) a ≤ -2 or a ≤ 4
(d) -2 ≤ a ≤ 4

Explaination:
(d), as $$\int_{0}^{a}$$ x dx ≤ a + 4
⇒ $$\frac{a²}{2}$$ ≤ a + 4
⇒ a² – 2a — 8 ≤ 0
⇒ (a – 1)² ≤ (3)²
⇒ -3 ≤ a – 1 ≤ 3
⇒ -2 ≤ a ≤ 4

14. If $$\frac{d}{dx}$$ f(x) = g(x), then antiderivative of g(x) is ________ .

Explaination:
f(x), as $$\frac{d}{dx}$$ f(x) = g(x)
⇒ ∫ g(x)dx = f(x).

15. Derivative of a function is unique but a function can have infinite antiderivatives. State true or false.

Explaination: True, as ∫ f(x)dx = g(x) + C, C is constant can take different values but $$\frac{d}{dx}$$ [g(x) + C]
=f(x) only

16.

Explaination: $$\frac{2}{3}$$ ∫ cosec x . cot x dx = –$$\frac{2}{3}$$ ∫ cosec x + C

17. Find ∫(ax + b)3dx [AI 2011]

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

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19. We have $$\frac{d}{dx}$$(3x² + sin x – ex) = 6x + cos x -ex. Represent the expression in the form of anti derivative.

Explaination:
$$\frac{d}{dx}$$ (3x² + sin x – ex) = 6x + cos x – ex
⇒ ∫ (6x + cos x – ex) = 3x² + sin x – ex

20.

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21.

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22. Evaluate ∫ (sin x + cos x)² dx

Explaination:
∫ (sin x + cos x)² dx = ∫ (sin²x + cos²x + 2sin x cos x)dx
= ∫(1 + sin 2x)dx = x – $$\frac{\cos 2 x}{2}$$ + C

23.

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24.

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

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26. Evaluate $$\int e^{\frac{1}{2} \log x} d x$$.

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27.

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

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28.

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29.

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30.

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31. Find ∫ sec² (7 – x)dx

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32. Find $$\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x$$

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33. Find ∫2x sin(x² + 1) dx

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34.

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35.

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36.

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37.

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38.

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39.

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40.

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41.

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42.

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43.

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44. Evaluate ∫ sec4 x tan x dx

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45.

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46.

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47. Find ∫ cot x . log(sin x) dx [NCERT]

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48.

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49. Find ∫(ex + 3x)² (ex + 3)dx

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50.

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51.

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52. Find ∫ (cosx – sinx)² dx

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53. Evaluate $$\int \sqrt{1+\sin \frac{x}{4}} d x$$

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54.

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55.

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56.

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57.

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58.

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59.

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

Explaination:
ex sec x, as ∫ex (sec x + sec x tan x) dx,
i.e. f(x) = sec x
f'(x) = sec x tan x,
using formula ∫ ex {f(x) + f'(x)}dx
= ex f(x) + C

61. If $$\int_{-1}^{4}$$ f(x) dx =4 and $$\int_{2}^{4}$$ (3 – f(x))dx = 7, then the value of $$\int_{-2}^{-1}$$ f(x) dx is ________ .

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62.

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63.

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64.

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65.

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66. If $$\int_{0}^{a}$$ 3x² dx = 8 write the value of a. [Foreign 2017]

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67. Evaluate. $$\int_{2}^{3}$$ 3x dx [Delhi 2017]

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68.

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69. $$\int_{0}^{2a}$$f(x)dx = 2 $$\int_{0}^{a}$$ f(x)dx if f(2a -x)= f(x). State true or false.

Explaination: True; result

70.

then value of a is ________ .

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71.

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72. $$\int_{-1}^{1}$$ |(1 – x)| dx is equal to ________ .

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73.

is equal to 0.State true or false.

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74. The value of $$\int_{0}^{\pi}$$ | cos x|dx is 2. State true or false.

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75. The value of $$\int_{-\pi}^{\pi}$$ sin3x cos²x dx is ________ .

Explaination: 0, as f(x) = sin3 x. cos² x dx is an odd function

76.

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77.

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78.

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79.

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80. Evaluate $$\int_{-1}^{1}$$ x|x|dx

Explaination:
Consider $$\int_{-1}^{1}$$ x|x| dx
f(x) = x|x|, f(-x) = (-x)|-x| = -x|x| = -f(x)
Odd function.
∴ $$\int_{-1}^{1}$$ x|x|dx = 0
[using $$\int_{-a}^{a}$$ f(x) = 0, if f(x) is odd function]

81. Evaluate $$\int_{0}^{2\pi}$$ cos5x dx [Foreign 2017]

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82.

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83. Evaluate $$\int_{0}^{1}$$ [2x]dx

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84. Evaluate $$\int_{1}^{4}$$ f(x) dx, where

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85.

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86. Evaluate $$\int_{-\pi}^{\pi}$$ (sin-93 x + x295) dx

Explaination:
$$\int_{-\pi}^{\pi}$$ (sin-93 x + x295)dx,f(x) is odd function as f(-x) = -f(x)
∴ $$\int_{-\pi}^{\pi}$$ (sin-93 x + x295) dx=0

87.

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88.

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89.

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90. $$\int_{1}^{e}$$ log x. dx

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91. Evaluate $$\int_{0}^{1}$$ x(1 – x)89dx

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92.

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93. Evaluate $$\int_{0}^{1}$$ x²(1 -x)ndx

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94.

95. Evaluate $$\int_{0}^{\pi}$$ |cos x|dx [DoE]