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Recent questions tagged integration
+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
(
434k
points)

95
views
isi2014dcg
calculus
definiteintegrals
integration
+2
votes
0
answers
2
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
(
434k
points)

33
views
isi2014dcg
calculus
integration
definiteintegrals
0
votes
0
answers
3
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
(
434k
points)

28
views
isi2014dcg
calculus
integration
definiteintegrals
0
votes
0
answers
4
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
(
434k
points)

44
views
isi2014dcg
calculus
integration
definiteintegrals
+1
vote
0
answers
5
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, 2019
in
Calculus
by
Arjun
Veteran
(
434k
points)

21
views
isi2015mma
integration
nongate
0
votes
1
answer
6
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, 2019
in
Calculus
by
gatecse
Boss
(
17.6k
points)

25
views
isi2015dcg
calculus
integration
0
votes
1
answer
7
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
(
17.6k
points)

28
views
isi2015dcg
integration
definiteintegrals
0
votes
0
answers
8
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, 2019
in
Calculus
by
gatecse
Boss
(
17.6k
points)

20
views
isi2016dcg
calculus
integration
nongate
0
votes
0
answers
9
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, 2019
in
Calculus
by
akash.dinkar12
Boss
(
42.7k
points)

85
views
isi2018mma
engineeringmathematics
calculus
integration
+1
vote
1
answer
10
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, 2019
in
Calculus
by
Sayan Bose
Loyal
(
7.5k
points)

414
views
isi2019mma
engineeringmathematics
calculus
integration
0
votes
1
answer
11
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, 2019
in
Calculus
by
Sayan Bose
Loyal
(
7.5k
points)

692
views
isi2019mma
calculus
engineeringmathematics
integration
0
votes
1
answer
12
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, 2019
in
Calculus
by
Sayan Bose
Loyal
(
7.5k
points)

258
views
isi2019mma
engineeringmathematics
calculus
integration
0
votes
0
answers
13
How to solve such question.
$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$
asked
Jan 20, 2019
in
Calculus
by
`JEET
Boss
(
19.4k
points)

103
views
calculus
integration
0
votes
0
answers
14
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, 2019
in
Calculus
by
jhaanuj2108
(
197
points)

96
views
acetestseries
calculus
integration
0
votes
0
answers
15
#integration
I=$\int_{1}^{\infty }a^{ceil (log _{b} x ) } dx$
asked
Jan 3, 2019
in
Calculus
by
amit166
Junior
(
783
points)

54
views
integration
0
votes
0
answers
16
#integration
$I=\int sin(2x) cos(3x) dx$ 1.(5cosxcos5x)/10 2.(5sinxsin5x)/10 3.both 4.none
asked
Jan 3, 2019
in
Calculus
by
amit166
Junior
(
783
points)

72
views
integration
+4
votes
2
answers
17
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
(
434k
points)

415
views
tifr2019
engineeringmathematics
calculus
integration
0
votes
0
answers
18
Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$
asked
Nov 22, 2018
in
Calculus
by
aditi19
Loyal
(
5.2k
points)

79
views
gilbertstrang
calculus
engineeringmathematics
integration
+2
votes
1
answer
19
CalculusIntegration
$\int x^7.e^{x^4}dx$ How to do this?
asked
Nov 22, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
30.6k
points)

128
views
calculus
integration
0
votes
1
answer
20
Integration
$\int_{0}^{1}\frac{x^{\alpha }1}{logx}dx$ where $\alpha>0$
asked
Nov 16, 2018
in
Calculus
by
srestha
Veteran
(
119k
points)

109
views
integration
calculus
engineeringmathematics
0
votes
0
answers
21
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^41}}$
asked
Nov 14, 2018
in
Calculus
by
aditi19
Loyal
(
5.2k
points)

58
views
gilbertstrang
calculus
engineeringmathematics
integration
0
votes
1
answer
22
Gilbert Strang
Differentiate y=$x^{1/lnx}$
asked
Oct 28, 2018
in
Calculus
by
aditi19
Loyal
(
5.2k
points)

47
views
gilbertstrang
calculus
integration
engineeringmathematics
0
votes
0
answers
23
Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$
asked
Oct 25, 2018
in
Calculus
by
aditi19
Loyal
(
5.2k
points)

81
views
gilbertstrang
calculus
integration
0
votes
1
answer
24
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
asked
Oct 24, 2018
in
Calculus
by
aditi19
Loyal
(
5.2k
points)

126
views
integration
calculus
engineeringmathematics
definiteintegrals
+1
vote
1
answer
25
CalculusDefinite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$
asked
Oct 13, 2018
in
Calculus
by
Ayush Upadhyaya
Boss
(
30.6k
points)

96
views
calculus
integration
engineeringmathematics
0
votes
1
answer
26
Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
asked
Oct 6, 2018
in
Calculus
by
srestha
Veteran
(
119k
points)

109
views
integration
calculus
engineeringmathematics
0
votes
0
answers
27
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
(
106k
points)

20
views
isi2016mmamma
calculus
integration
definiteintegrals
0
votes
1
answer
28
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)

62
views
engineeringmathematics
integration
+1
vote
1
answer
29
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
(
17.6k
points)

181
views
calculus
integration
engineeringmathematics
integrals
0
votes
0
answers
30
Integration
$f\left ( x \right )=$\int_{2}^{2}x^{\frac{2}{7}}dx$ Is this function f(x) is continuous, bounded and differentiable? (In exam hall is it possible to draw the graph for this function f(x), or some other procedure to follow to ans this)
asked
May 18, 2018
in
Calculus
by
srestha
Veteran
(
119k
points)

223
views
integration
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