Definite Integration · Mathematics · NDA
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?
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?
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 $\int^{1}_{-1}(3\sin x-\sin 3x)\cos^2 xdx$ equal to?
NDA Mathematics 21 April 2024
39
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
40
What is $\int^{\pi/2}_0 \frac{a+\sin x}{2a+\sin x+\cos x} dx$ equal to?
NDA Mathematics 21 April 2024
41
What is $\int\limits_{-1}^{0} h(x) dx$ equal to?
NDA Mathematics 21 April 2024
42
What is $\int_{0}^{2} h(x) dx$ equal to?
NDA Mathematics 21 April 2024
43
What is $8\int_1^2 f(x)dx$ equal to?
NDA Mathematics 21 April 2024
44
What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?
NDA Mathematics 3 September 2023
45
What is I equal to?
NDA Mathematics 3 September 2023
46
What is $\displaystyle \rm \int_0^{8 \pi}|\sin x| d x$ equal to?
NDA Mathematics 3 September 2023
47
‘What is the value of Q ?
NDA Mathematics 16 April 2023
48
What is the value of R ?
NDA Mathematics 16 April 2023
49
What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ?
NDA Mathematics 16 April 2023
50
What is the value of $8 I_1^2$
NDA Mathematics 16 April 2023
51
What is the value of I2 ?
NDA Mathematics 16 April 2023
52
What is l equal to when a < 0 < b ?
NDA Mathematics 16 April 2023
53
What is l equal to when a < b < 0 ?
NDA Mathematics 16 April 2023
54
What is $\displaystyle\int_0^1 \ln \left(\frac{1}{x}−1\right)$dx equal to ?
NDA Mathematics 4 September 2022
55
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
56
What is $\displaystyle\int_{−\pi/2}^{\pi/2}$(ecos x sin x + esin x cos x)dx equal to ?
NDA Mathematics 4 September 2022
57
What is $\int\limits^{\frac{\pi}{4}}_0 \frac{dx}{(\sin x + \cos x)^2}$ equal to?
NDA Mathematics 10 April 2022
58
What is $\int\limits^{-1}_{-2}\frac{x}{|x|}dx$ equal to?
NDA Mathematics 10 April 2022
59
If f(x) satisfies f(1) = f(4), then what is $\rm \int^4_1f'(x) dx$ equal to?
NDA Mathematics 14 November 2021
60
What is $\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx$ equal to?
NDA Mathematics 14 November 2021
61
What is $\rm \int^\pi _0 ln\left(tan\frac{x}{2}\right) dx$ equal to?
NDA Mathematics 14 November 2021
62
If f(x) = 2x, then what is $\int^{10}_2\frac{f'(x)}{f(x)}dx$ equal to?
NDA Mathematics 14 November 2021
63
If $\rm \int^0_{-2} f(x)dx=k$, then $\rm \int^0_{-2}|f(x)|dx$ is
NDA Mathematics 14 November 2021
64
What is $\rm \int_0^a \frac{f(a-x)}{f(x)+f(a-x)}\ dx $ equal to?
NDA Mathematics 18 April 2021
65
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