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Recent questions tagged definiteintegrals
+2
votes
1
answer
1
ISI2014DCG12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

83
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isi2014dcg
calculus
definiteintegrals
integration
0
votes
1
answer
2
ISI2014DCG20
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, 2019
in
Geometry
by
Arjun
Veteran
(
431k
points)

28
views
isi2014dcg
calculus
definiteintegrals
area
+2
votes
0
answers
3
ISI2014DCG31
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

28
views
isi2014dcg
calculus
integration
definiteintegrals
0
votes
0
answers
4
ISI2014DCG47
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

19
views
isi2014dcg
calculus
integration
definiteintegrals
0
votes
0
answers
5
ISI2014DCG53
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

31
views
isi2014dcg
calculus
integration
definiteintegrals
0
votes
0
answers
6
ISI2015MMA69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ 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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

19
views
isi2015mma
calculus
continuity
differentiation
definiteintegrals
nongate
0
votes
0
answers
7
ISI2015MMA76
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

13
views
isi2015mma
calculus
definiteintegrals
nongate
0
votes
1
answer
8
ISI2015MMA78
The value of $\displaystyle \lim_{n \to \infty} \left[ (n+1) \int_0^1 x^n \ln(1+x) dx \right]$ is $0$ $\ln 2$ $\ln 3$ $\infty$
asked
Sep 23, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

18
views
isi2015mma
calculus
limits
definiteintegrals
nongate
0
votes
0
answers
9
ISI2015MMA80
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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

21
views
isi2015mma
calculus
definiteintegrals
summation
nongate
0
votes
0
answers
10
ISI2015MMA81
If $f$ is continuous in $[0,1]$ then $\displaystyle \lim_ {n \to \infty} \sum_{j=0}^{[n/2]} \frac{1}{n} f \left(\frac{j}{n} \right)$ (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, 2019
in
Calculus
by
Arjun
Veteran
(
431k
points)

17
views
isi2015mma
limits
definiteintegrals
nongate
0
votes
1
answer
11
ISI2015DCG51
The area bounded by $y=x^24$, $y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
asked
Sep 18, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

21
views
isi2015dcg
integration
definiteintegrals
0
votes
1
answer
12
ISI2017DCG25
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

39
views
isi2017dcg
linearalgebra
determinant
definiteintegrals
nongate
0
votes
1
answer
13
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
asked
Oct 24, 2018
in
Calculus
by
aditi19
Active
(
5.2k
points)

120
views
integration
calculus
engineeringmathematics
definiteintegrals
0
votes
0
answers
14
ISI2016MMA23
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)

14
views
isi2016mmamma
calculus
integration
definiteintegrals
+1
vote
0
answers
15
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
(
1.3k
points)

120
views
engineeringmathematics
calculus
integration
definiteintegrals
virtualgatetestseries
+2
votes
3
answers
16
integration
$\int_{4}^{4}3xdx$ a) 13 b)8 c)25 d)24
asked
Nov 11, 2017
in
Calculus
by
Parshu gate
Active
(
3.1k
points)

210
views
engineeringmathematics
calculus
integration
definiteintegrals
+2
votes
1
answer
17
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)

654
views
integration
definiteintegrals
calculus
engineeringmathematics
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