The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register
|
I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Recent questions tagged definite-integration
0
votes
1
answer
1
ISI2014-DCG-20
If $A(t)$ is the area of the region bounded by the curve $y=e^{-\mid x \mid}$ and the portion of the $x$-axis between $-t$ and $t$, then $\underset{t \to \infty}{\lim} A(t)$ equals $0$ $1$ $2$ $4$
asked
Sep 23
in
Others
by
Arjun
Veteran
(
425k
points)
|
21
views
isi2014-dcg
calculus
integration
definite-integration
area
+2
votes
0
answers
2
ISI2014-DCG-31
For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
20
views
isi2014-dcg
calculus
integration
definite-integration
0
votes
0
answers
3
ISI2014-DCG-47
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is $\frac{\pi}{6} + \sqrt{3}$ $\frac{\pi}{6} - \sqrt{3}$ $0$ $\frac{1}{2}$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
11
views
isi2014-dcg
calculus
integration
definite-integration
0
votes
0
answers
4
ISI2014-DCG-53
The value of the integral $\displaystyle{}\int_{-1}^1 \dfrac{x^2}{1+x^2} \sin x \sin 3x \sin 5x dx$ is $0$ $\frac{1}{2}$ $ – \frac{1}{2}$ $1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
21
views
isi2014-dcg
calculus
integration
definite-integration
0
votes
0
answers
5
ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
9
views
isi2015-mma
calculus
continuity
differentiability
definite-integration
non-gate
0
votes
0
answers
6
ISI2015-MMA-76
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$ is $\sqrt{\pi/3}$ $\pi/\sqrt{3}$ $\sqrt{2 \pi/3}$ $2 \pi / \sqrt{3}$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
7
views
isi2015-mma
calculus
definite-integration
non-gate
0
votes
1
answer
7
ISI2015-MMA-78
The value of $\underset{n \to \infty}{\lim} \bigg[ (n+1) \int_0^1 x^n \text{ln}(1+x) dx \bigg]$ is $0$ $\text{ln }2$ $\text{ln }3$ $\infty$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
8
views
isi2015-mma
calculus
limits
definite-integration
non-gate
0
votes
0
answers
8
ISI2015-MMA-80
Let $0 < \alpha < \beta < 1$. Then $ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$ is equal to $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
14
views
isi2015-mma
calculus
definite-integration
summation
non-gate
0
votes
0
answers
9
ISI2015-MMA-81
If $f$ is continuous in $[0,1]$ then $\underset{n \to \infty}{\lim} \Sigma_{j=0}^{[n/2]} \frac{1}{n} f \bigg(\frac{j}{n} \bigg)$ (where $[y]$ is the largest integer less than or equal to $y$) does not exist exists and is equal to $\frac{1}{2} \int_0^1 f(x) dx$ exists and is equal to $ \int_0^1 f(x) dx$ exists and is equal to $\int_0^{1/2} f(x) dx$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)
|
8
views
isi2015-mma
limits
continuity
definite-integration
non-gate
0
votes
1
answer
10
ISI2015-DCG-51
The area bounded by $y=x^2-4$, $y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)
|
12
views
isi2015-dcg
integration
definite-integration
area
0
votes
0
answers
11
ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)
|
9
views
isi2017-dcg
linear-algebra
determinant
definite-integration
differentiation
0
votes
1
answer
12
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
asked
Oct 24, 2018
in
Calculus
by
aditi19
Active
(
5.1k
points)
|
112
views
integration
calculus
engineering-mathematics
definite-integration
0
votes
0
answers
13
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
asked
Sep 13, 2018
in
Calculus
by
jothee
Veteran
(
105k
points)
|
9
views
isi2016-mmamma
calculus
integration
definite-integration
+1
vote
0
answers
14
Virtual Gate Test Series: Calculus - Definite Integration
$\int \limits_0^1 (1 + y^2)^{-1.5} dy=?$
asked
Jan 31, 2018
in
Calculus
by
Utsav09
Active
(
1.2k
points)
|
110
views
engineering-mathematics
calculus
integration
definite-integration
virtual-gate-test-series
+2
votes
3
answers
15
integration
$\int_{-4}^{4}|3-x|dx$ a) 13 b)8 c)25 d)24
asked
Nov 11, 2017
in
Calculus
by
Parshu gate
Active
(
3.1k
points)
|
202
views
engineering-mathematics
calculus
integration
definite-integration
+2
votes
1
answer
16
integration question
$f(x) = \int_{- \infty}^{\infty} f(x) e^{2\pi x} dx$ solve f(x)
asked
Oct 11, 2017
in
Calculus
by
Pavan Kumar Munnam
Boss
(
10.7k
points)
|
621
views
integration
definite-integration
calculus
engineering-mathematics
To see more, click for the
full list of questions
or
popular tags
.
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Linear Algebra Important Points
GATE 2020
OFFICIAL GATE MOCK TEST RELEASED
IIITH: Winter Research Admissions 2019 (For Spring 2020)
TIFR and JEST exam
Follow @csegate
Recent questions tagged definite-integration
Recent Blog Comments
Arjun sir, plz provide go book through...
@
[email protected]
Can this be updated?
Even In 2019 my 16 questions goes for negative...
i also don't have any pdf, actually, I added the...
i don't have , if you have upload it
50,647
questions
56,508
answers
195,519
comments
100,954
users