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Recent questions tagged definite-integral
5
votes
1
answer
1
GATE CSE 2024 | Set 2 | Question: 6
Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x)=1-f(2-x) \] Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$
Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that\[f(x)=1-f(2-x)\]Which one of the following options is the CORRECT value of ...
Arjun
2.3k
views
Arjun
asked
Feb 16
Calculus
gatecse2024-set2
calculus
definite-integral
+
–
5
votes
2
answers
2
GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)
The value of the definite integral \[\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x\]is _________. (Rounde...
admin
8.9k
views
admin
asked
Feb 15, 2023
Calculus
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
+
–
1
votes
1
answer
3
NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$$16/1155$$16/385$$16\pi/385$$8\pi/385$
admin
359
views
admin
asked
Apr 2, 2020
Calculus
nielit2016mar-scientistc
engineering-mathematics
calculus
definite-integral
+
–
0
votes
1
answer
4
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 19
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is $(x+2)/2$ $2/(\pi-2)$ $\pi – 2$ $\pi + 2$
The value of the Integral $I = \displaystyle{}\int_{0}^{\pi/2} x^{2}\sin x dx$ is$(x+2)/2$$2/(\pi-2)$$\pi – 2$$\pi + 2$
admin
479
views
admin
asked
Apr 1, 2020
Calculus
nielit2017oct-assistanta-cs
engineering-mathematics
calculus
definite-integral
+
–
1
votes
1
answer
5
NIELIT 2016 MAR Scientist B - Section B: 9
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$ $1/4$ $0$ $-1/4$ $1$
The value of improper integral $\displaystyle\int_{0}^{1} x\ln x =?$$1/4$$0$$-1/4$$1$
admin
738
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
+
–
1
votes
2
answers
6
NIELIT 2016 MAR Scientist B - Section B: 11
What is the derivative w.r.t $x$ of the function given by $\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$, $2x^2$ $\sqrt x$ $0$ $1$
What is the derivative w.r.t $x$ of the function given by$\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$,$2x^2$$\sqrt x$$0$$1$
admin
545
views
admin
asked
Mar 31, 2020
Calculus
nielit2016mar-scientistb
engineering-mathematics
calculus
integration
definite-integral
+
–
2
votes
1
answer
7
ISI2014-DCG-12
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
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
Arjun
729
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
definite-integral
integration
+
–
0
votes
1
answer
8
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 $0$ $1$ $2$ $4$
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(...
Arjun
349
views
Arjun
asked
Sep 23, 2019
Geometry
isi2014-dcg
calculus
definite-integral
area
+
–
3
votes
1
answer
9
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 $\alpha$ $[\alpha]$ $1$ $\dfrac{[\alpha] + [\alpha +1]}{2}$
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$$\dfrac{[\alph...
Arjun
589
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
integration
definite-integral
+
–
1
votes
1
answer
10
ISI2014-DCG-47
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is $\frac{\pi}{6} + \sqrt{3}$ $\frac{\pi}{6} - \sqrt{3}$ $0$ $\frac{1}{2}$
The value of the definite integral $\int_0^{\pi} \mid \frac{1}{2} + \cos x \mid dx$ is$\frac{\pi}{6} + \sqrt{3}$$\frac{\pi}{6} - \sqrt{3}$$0$$\frac{1}{2}$
Arjun
519
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
integration
definite-integral
+
–
0
votes
1
answer
11
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}$ $1$
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}$$1$
Arjun
609
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
integration
definite-integral
+
–
0
votes
2
answers
12
ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
Consider the function $$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}$$ Then$f$ is not continuous at...
Arjun
835
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
+
–
0
votes
1
answer
13
ISI2015-MMA-76
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$ is $\sqrt{\pi/3}$ $\pi/\sqrt{3}$ $\sqrt{2 \pi/3}$ $2 \pi / \sqrt{3}$
Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $$ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$$ is$\sqrt{\pi/3}$$...
Arjun
454
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
definite-integral
non-gate
+
–
0
votes
2
answers
14
ISI2015-MMA-78
The value of $\displaystyle \lim_{n \to \infty} \left[ (n+1) \int_0^1 x^n \ln(1+x) dx \right]$ is $0$ $\ln 2$ $\ln 3$ $\infty$
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$$\infty$
Arjun
517
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
limits
definite-integral
non-gate
+
–
0
votes
0
answers
15
ISI2015-MMA-80
Let $0 < \alpha < \beta < 1$. Then $ \Sigma_{k=1}^{\infty} \int_{1/(k+\beta)}^{1/(k+\alpha)} \frac{1}{1+x} dx$ is equal to $\log_e \frac{\beta}{\alpha}$ $\log_e \frac{1+ \beta}{1 + \alpha}$ $\log_e \frac{1+\alpha }{1+ \beta}$ $\infty$
Let $0 < \alpha < \beta < 1$. Then $$ \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+ ...
Arjun
520
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
definite-integral
summation
non-gate
+
–
1
votes
1
answer
16
ISI2015-MMA-81
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 $\int_0^{1/2} f(x) dx$
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 integ...
Arjun
421
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
limits
definite-integral
non-gate
+
–
1
votes
1
answer
17
ISI2015-DCG-51
The area bounded by $y=x^2-4$, $y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
The area bounded by $y=x^2-4$, $y=0$ and $x=4$ is$\frac{64}{3}$$6$$\frac{16}{3}$$\frac{32}{3}$
gatecse
424
views
gatecse
asked
Sep 18, 2019
Calculus
isi2015-dcg
integration
definite-integral
+
–
1
votes
1
answer
18
ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [...
gatecse
588
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2017-dcg
linear-algebra
determinant
definite-integral
non-gate
+
–
7
votes
2
answers
19
TIFR CSE 2019 | Part A | Question: 13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
Consider the integral$$\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$$1.00$
Arjun
2.8k
views
Arjun
asked
Dec 18, 2018
Calculus
tifr2019
engineering-mathematics
calculus
definite-integral
+
–
0
votes
1
answer
20
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
aditi19
494
views
aditi19
asked
Oct 24, 2018
Calculus
integration
calculus
engineering-mathematics
definite-integral
+
–
0
votes
0
answers
21
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?$0$$\sqrt{\pi}...
go_editor
446
views
go_editor
asked
Sep 13, 2018
Calculus
isi2016-mmamma
calculus
integration
definite-integral
+
–
1
votes
0
answers
22
Virtual Gate Test Series: Calculus - Definite Integration
$\int \limits_0^1 (1 + y^2)^{-1.5} dy=?$
$\int \limits_0^1 (1 + y^2)^{-1.5} dy=?$
Utsav09
495
views
Utsav09
asked
Jan 31, 2018
Calculus
engineering-mathematics
calculus
integration
definite-integral
virtual-gate-test-series
+
–
2
votes
3
answers
23
integration
$\int_{-4}^{4}|3-x|dx$ a) 13 b)8 c)25 d)24
$\int_{-4}^{4}|3-x|dx$a) 13 b)8 c)25 d)24
Parshu gate
735
views
Parshu gate
asked
Nov 11, 2017
Calculus
engineering-mathematics
calculus
integration
definite-integral
+
–
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