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Recent questions tagged integration
0
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
in
Calculus
by
Arjun
Veteran
(
425k
points)

63
views
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
in
Others
by
Arjun
Veteran
(
425k
points)

22
views
isi2014dcg
calculus
integration
definiteintegration
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
in
Calculus
by
Arjun
Veteran
(
425k
points)

20
views
isi2014dcg
calculus
integration
definiteintegration
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
in
Calculus
by
Arjun
Veteran
(
425k
points)

12
views
isi2014dcg
calculus
integration
definiteintegration
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
in
Calculus
by
Arjun
Veteran
(
425k
points)

21
views
isi2014dcg
calculus
integration
definiteintegration
+1
vote
0
answers
6
ISI2015MMA77
Let $R$ be the triangle in the $xy$ – plane bounded by the $x$axis, the line $y=x$, and the line $x=1$. The value of the double integral $ \int \int_R \frac{\sin x}{x}\: dxdy$ is $1\cos 1$ $\cos 1$ $\frac{\pi}{2}$ $\pi$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
425k
points)

8
views
isi2015mma
integration
nongate
0
votes
1
answer
7
ISI2015DCG46
Let $I=\int (\sin x – \cos x)(\sin x + \cos x)^3 dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin x + \cos x)^4+K$ $(\sin x + \cos x)^2+K$ $ \frac{1}{4} (\sin x + \cos x)^4+K$ None of these
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

16
views
isi2015dcg
calculus
integration
0
votes
1
answer
8
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
in
Calculus
by
gatecse
Boss
(
16.8k
points)

12
views
isi2015dcg
integration
definiteintegration
area
0
votes
0
answers
9
ISI2016DCG46
Let $I=\int(\sin\:x\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is $(\sin\:x+\cos\:x)^{4}+K$ $(\sin\:x+\cos\:x)^{2}+K$ $\frac{1}{4}(\sin\:x+\cos\:x)^{4}+K$ None of these
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

12
views
isi2016dcg
calculus
integration
trigonometry
0
votes
0
answers
10
ISI2018MMA29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $2$ $1$ $1$ $2$
asked
May 11
in
Calculus
by
akash.dinkar12
Boss
(
41.9k
points)

57
views
isi2018mma
engineeringmathematics
calculus
integration
+1
vote
1
answer
11
ISI2019MMA29
Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\psi(y) =0$ for all $y \notin [0,1]$ and $\int_{0}^{1} \psi(y) dy=1$. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function. Then the value of $\lim _{n\rightarrow \infty}n \int_{0}^{100} f(x)\psi(nx)dx$ is $f(0)$ $f’(0)$ $f’’(0)$ $f(100)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7.2k
points)

388
views
isi2019mma
engineeringmathematics
calculus
integration
0
votes
1
answer
12
ISI2019MMA28
Consider the functions $f,g:[0,1] \rightarrow [0,1]$ given by $f(x)=\frac{1}{2}x(x+1) \text{ and } g(x)=\frac{1}{2}x^2(x+1).$ Then the area enclosed between the graphs of $f^{1}$ and $g^{1}$ is $1/4$ $1/6$ $1/8$ $1/24$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7.2k
points)

646
views
isi2019mma
calculus
engineeringmathematics
integration
0
votes
1
answer
13
ISI2019MMA25
Let $a,b,c$ be nonzero real numbers such that $\int_{0}^{1} (1 + \cos^8x)(ax^2 + bx +c)dx = \int_{0}^{2}(1+ \cos^8x)(ax^2 + bx + c) dx =0$ Then the quadratic equation $ax^2 + bx +c=0$ has no roots in $(0,2)$ one root in $(0,2)$ and one root outside this interval one repeated root in $(0,2)$ two distinct real roots in $(0,2)$
asked
May 7
in
Calculus
by
Sayan Bose
Loyal
(
7.2k
points)

236
views
isi2019mma
engineeringmathematics
calculus
integration
0
votes
0
answers
14
How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
asked
Jan 20
in
Calculus
by
`JEET
Boss
(
13.8k
points)

97
views
calculus
integration
0
votes
0
answers
15
Ace Test Series: Calculus  Integration
Can anyone help me with solving this type of problem? I want some resource from where I can learn to solve this type on integration, as according to solution it is a function of α, so I did not understand the solution.
asked
Jan 12
in
Calculus
by
jhaanuj2108
(
197
points)

82
views
acetestseries
calculus
integration
0
votes
0
answers
16
#integration
I=$\int_{1}^{\infty }a^{ceil (log _{b} x ) } dx$
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

50
views
integration
0
votes
0
answers
17
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosxcos5x)/10 2.(5sinxsin5x)/10 3.both 4.none
asked
Jan 3
in
Calculus
by
amit166
Junior
(
761
points)

68
views
integration
+3
votes
2
answers
18
TIFR2019A13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
asked
Dec 18, 2018
in
Calculus
by
Arjun
Veteran
(
425k
points)

327
views
tifr2019
engineeringmathematics
calculus
integration
0
votes
0
answers
19
Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$
asked
Nov 22, 2018
in
Calculus
by
aditi19
Active
(
5.1k
points)

76
views
gilbertstrang
calculus
engineeringmathematics
integration
+2
votes
1
answer
20
CalculusIntegration
$\int x^7.e^{x^4}dx$ How to do this?
asked
Nov 22, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
27.8k
points)

119
views
calculus
integration
0
votes
1
answer
21
Integration
$\int_{0}^{1}\frac{x^{\alpha }1}{logx}dx$ where $\alpha>0$
asked
Nov 16, 2018
in
Calculus
by
srestha
Veteran
(
117k
points)

99
views
integration
calculus
engineeringmathematics
0
votes
0
answers
22
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^41}}$
asked
Nov 14, 2018
in
Calculus
by
aditi19
Active
(
5.1k
points)

50
views
gilbertstrang
calculus
engineeringmathematics
integration
0
votes
1
answer
23
Gilbert Strang
Differentiate y=$x^{1/lnx}$
asked
Oct 28, 2018
in
Calculus
by
aditi19
Active
(
5.1k
points)

43
views
gilbertstrang
calculus
integration
engineeringmathematics
0
votes
0
answers
24
Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$
asked
Oct 25, 2018
in
Calculus
by
aditi19
Active
(
5.1k
points)

71
views
gilbertstrang
calculus
integration
0
votes
1
answer
25
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
engineeringmathematics
definiteintegration
+1
vote
1
answer
26
CalculusDefinite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$
asked
Oct 13, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
27.8k
points)

85
views
calculus
integration
engineeringmathematics
0
votes
1
answer
27
Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
asked
Oct 6, 2018
in
Calculus
by
srestha
Veteran
(
117k
points)

101
views
integration
calculus
engineeringmathematics
0
votes
0
answers
28
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)

9
views
isi2016mmamma
calculus
integration
definiteintegration
0
votes
1
answer
29
Area between curves
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is . I am getting $128√2$.
asked
Sep 3, 2018
in
Calculus
by
Jason
Active
(
1.5k
points)

45
views
engineeringmathematics
integration
+1
vote
1
answer
30
Definite Integral
S = $\int_{0}^{2\Pi } \sqrt{4cos^{2}t +sin^{2}t} \, \, dt$ Please explain how to solve it.
asked
Jun 11, 2018
in
Calculus
by
ankitgupta.1729
Boss
(
16.4k
points)

151
views
calculus
integration
engineeringmathematics
integrals
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