Definite Integration · Mathematics · NDA

Start Practice

MCQ (Single Correct Answer)

1
The value of $$\int_a^b {{{{x^7} + \sin x} \over {\cos x}}} dx$$, where a + b = 0, is
NDA 2015 Paper 2
2
If 0 < a < b, then $$\int_a^b {{{|x|} \over x}} dx$$ is equal to
NDA 2015 Paper 2
3
$$\int_0^{2\pi } {{{\sin }^5}\left( {{x \over 4}} \right)dx} $$ is equal to
NDA 2015 Paper 2
4
$$\int_{ - 1}^1 {x|x|} \,dx$$ is equal to
NDA 2015 Paper 2
5
Which one of the following is correct?
NDA 2015 Paper 2
6
What is the value of B?
NDA 2015 Paper 2
7
What is I1 equal to ?
NDA 2015 Paper 2
8
What I2 + I3 equal to ?
NDA 2015 Paper 2
9
What is Im equal to ?
NDA 2015 Paper 2
10
Consider the following

I. Im $$-$$ Im $$-$$ 1 is equal to 0

II. I2m > Im

Which of the above is/are correct?
NDA 2015 Paper 2
11
Let f(x) be a function such that $$f'\left( {{1 \over x}} \right) + {x^3}f'(x) = 0$$. What is $$\int_{ - 1}^1 {f(x)} \,dx$$ equal to ?
NDA 2016 Paper 2
12
If $$\int_0^{\pi /2} {{{dx} \over {3\cos x + 5}} = k{{\cot }^{ - 1}}2} $$, then what is the value of k?
NDA 2016 Paper 2
13
What is $$\int_1^3 {\left| {1 - {x^4}} \right|} \,dx$$ equal to ?
NDA 2016 Paper 2
14
What is $$\int_{1/3}^{1/2} {g(x)\,dx} $$ equal to ?
NDA 2016 Paper 1
15
What is $$\int_{1/3}^1 {f(x)} \,dx$$ equal to ?
NDA 2016 Paper 1
16
Consider the following statements

1. The sequence $$\{ {a_{2n}}\} $$ is in AP with common difference zero.

2. The sequence $$\{ {a_{2n + 1}}\} $$ is in AP with common difference zero.

Which of the above statements is/are correct?
NDA 2016 Paper 1
17
What is $${a_{n - 1}} - {a_{n - 4}}$$ equal to ?
NDA 2016 Paper 1
18
What is $$\int_{ - 2}^2 {x\,dx - \int_{ - 2}^2 {[x]} \,dx} $$ equal to, where [ . ] is the greatest integer function?
NDA 2016 Paper 1
19
If $$\int_{ - 2}^5 {f(x)dx = 4} $$ and $$\int_0^5 {\{ 1 + f(x)\} dx} = 7$$, then what is $$\int_{ - 2}^0 {f(x)dx} $$ equal to ?
NDA 2016 Paper 1
20
What is $$\int_0^{4\pi } {\left| {\cos x} \right|} \,dx$$ equal to ?
NDA 2016 Paper 1
21
What is $$\int\limits_0^{2\pi } {\sqrt {1 + \sin {x \over 2}} dx} $$ equal to ?
NDA 2017 Paper 2
22
The value of $$\int_0^{{\pi \over 4}} {\sqrt {\tan x} dx + \int_0^{{\pi \over 4}} {\sqrt {\cot x} dx} } $$ is equal to
NDA 2017 Paper 2
23
What is $$\int_0^{{\pi \over 2}} {{{d\theta } \over {1 + \cos \theta }}} $$ equal to ?
NDA 2017 Paper 1
24
If f(x) and g(x) are continuous functions satisfying f(x) = f(a $$-$$ x) and g(x) + g(a $$-$$ x) = 2, then what is $$\int_0^a {f(x)g(x)dx} $$ equal to ?
NDA 2017 Paper 1
25
What is $$\int_{{e^{ - 1}}}^{{e^2}} {\left| {{{\ln x} \over x}} \right|} dx$$ equal to ?
NDA 2017 Paper 1
26
What is $$\int_a^b {[x]dx + \int_a^b {[ - x]dx} } $$ equal to, where [ , ] is the greatest integer function?
NDA 2018 Paper 2
27
What is $$\int\limits_{ - 1}^1 {\left\{ {{d \over {dx}}\left( {{{\tan }^{ - 1}}{1 \over x}} \right)} \right\}} dx$$ equal to ?
NDA 2018 Paper 2
28
What is $$\int\limits_0^\pi {{e^x}\sin x} \,dx$$ equal to ?
NDA 2018 Paper 1
29
What is $$\int\limits_1^e x \ln x\,dx$$ equal to ?
NDA 2018 Paper 1
30
What is $$\int\limits_0^{\sqrt 2 } {[{x^2}]} \,dx$$ equal to (where [ . ] is the greatest integer function) ?
NDA 2018 Paper 1
31
what is the value of $$\int\limits_{ - \pi /4}^{\pi /4} {(\sin x - \tan x)\,dx} $$ ?
NDA 2018 Paper 1
32
If $$\int\limits_a^b {{x^3}} dx = 0$$ and $$\int\limits_a^b {{x^2}} dx = {2 \over 3}$$, then what are the values of a and b respectively ?
NDA 2018 Paper 1
33
What is $$\int\limits_0^1 {x{{(1 - x)}^9}} dx$$ equal to ?
NDA 2018 Paper 1
34
What is the value of I1 ?
NDA 2019 Paper 2
35
What is the value of I1 + I2 ?
NDA 2019 Paper 2
36
$$\int_0^{{\pi \over 2}} {\left| {\sin x - \cos x} \right|} \,dx$$ is equal to
NDA 2019 Paper 1
37
$$\int_0^{{\pi \over 2}} {{e^{\sin x}}} \cos x\,xdx$$ is equal to
NDA 2019 Paper 1
38
What is $\rm \int_0^2f(x)dx$ equal to
NDA Mathematics 1st September 2024
39
What is $\rm \int_h^3f(x)dx$ equal to
NDA Mathematics 1st September 2024
40
What is $\rm \int_{-\pi}^\pi g(t)dt$ equal to
NDA Mathematics 1st September 2024
41
What is $\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}$ equal to
NDA Mathematics 1st September 2024
42
What is I equal to?
NDA Mathematics 1st September 2024
43

What is $\int^{1}_{-1}(3\sin x-\sin 3x)\cos^2 xdx$ equal to?

NDA Mathematics 21 April 2024
44
Let $p=\int_a^b f(x) d x$ and $q=\int_a^b|f(x)| d x$. If $f(x)=e^{-x}$, then which one of the following is correct ?
NDA Mathematics 21 April 2024
45

What is $\int^{\pi/2}_0 \frac{a+\sin x}{2a+\sin x+\cos x} dx$ equal to?

NDA Mathematics 21 April 2024
46

What is $\int\limits_{-1}^{0} h(x) dx$ equal to?

NDA Mathematics 21 April 2024
47

What is $\int_{0}^{2} h(x) dx$ equal to?

NDA Mathematics 21 April 2024
48

What is $8\int_1^2 f(x)dx$ equal to?

NDA Mathematics 21 April 2024
49
What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?
NDA Mathematics 3 September 2023
50
What is I equal to?
NDA Mathematics 3 September 2023
51
What is $\displaystyle \rm \int_0^{8 \pi}|\sin x| d x$ equal to?
NDA Mathematics 3 September 2023
52
‘What is the value of Q ? 
NDA Mathematics 16 April 2023
53
What is the value of R ? 
NDA Mathematics 16 April 2023
54
What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ?
NDA Mathematics 16 April 2023
55
What is the value of $8 I_1^2$
NDA Mathematics 16 April 2023
56
What is the value of I2 ?
NDA Mathematics 16 April 2023
57
What is l equal to when a < 0 < b ? 
NDA Mathematics 16 April 2023
58
What is l equal to when a < b < 0 ? 
NDA Mathematics 16 April 2023
59
What is $\displaystyle\int_0^1 \ln \left(\frac{1}{x}−1\right)$dx equal to ?
NDA Mathematics 4 September 2022
60
If $\displaystyle\int_0^{\pi/2}$(sin4 x + cos4 x)dx = k, then what is the value of $\displaystyle\int_0^{20 \pi}$(sin4 x + cos4 x)dx ?
NDA Mathematics 4 September 2022
61
What is $\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x sin x + esin x cos x)dx equal to ?
NDA Mathematics 4 September 2022
62
What is $\int\limits^{\frac{\pi}{4}}_0 \frac{dx}{(\sin x + \cos x)^2}$ equal to?
NDA Mathematics 10 April 2022
63
What is $\int\limits^{-1}_{-2}\frac{x}{|x|}dx$ equal to?
NDA Mathematics 10 April 2022
64
If f(x) satisfies f(1) = f(4), then what is $\rm \int^4_1f'(x) dx$ equal to?
NDA Mathematics 14 November 2021
65
What is $\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx$ equal to?
NDA Mathematics 14 November 2021
66
What is $\rm \int^\pi _0 ln\left(tan\frac{x}{2}\right) dx$ equal to?
NDA Mathematics 14 November 2021
67
If f(x) = 2x, then what is $\int^{10}_2\frac{f'(x)}{f(x)}dx$ equal to?
NDA Mathematics 14 November 2021
68
If $\rm \int^0_{-2} f(x)dx=k$, then $\rm \int^0_{-2}|f(x)|dx$ is
NDA Mathematics 14 November 2021
69

What is $\rm \int_0^a \frac{f(a-x)}{f(x)+f(a-x)}\ dx $ equal to?

NDA Mathematics 18 April 2021
70

If $\rm \int_0^a \left[f(x)+f(-x)\right]dx=\int_{-a}^{\ \ a} g(x)\ dx $, then what is g(x) equal to?

NDA Mathematics 18 April 2021
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12