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Recent questions tagged definite-integrals
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GATE Mechanical 2021 Set 2 | Question: 26
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$
go_editor
asked
in
Calculus
Mar 1, 2021
by
go_editor
5.0k
points
gateme-2021-set2
calculus
definite-integrals
double-interals
0
answers
0
votes
GATE2020-ME-2: 3
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$
go_editor
asked
in
Calculus
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
calculus
definite-integrals
double-interals
1
answer
0
votes
GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
Arjun
asked
in
Calculus
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set1
numerical-answers
calculus
definite-integrals
0
answers
0
votes
GATE ME 2012 | Question: 11
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is $1/6$ $1/4$ $1/3$ $1/2$
Andrijana3306
asked
in
Calculus
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
calculus
definite-integrals
area-under-curve
0
answers
0
votes
GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
Arjun
asked
in
Calculus
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set1
calculus
mean-value-theorems
definite-integrals
0
answers
1
vote
GATE2016-1-28
The value of the integral $\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$ evaluated using contour integration and the residue theorem is $\displaystyle{\frac{-\pi \sin(1)}{e}}\\$ $\displaystyle{\frac{-\pi \cos (1)}{e}} \\$ $\displaystyle{\frac{\sin (1)}{e}} \\$ $\displaystyle{\frac{\cos (1)}{e}}$
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set1
calculus
definite-integrals
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 27
The value of the integral $\int_{0}^{2}\int_{0}^{x}e^{x+y}dydx$ is $\dfrac{1}{2}(e-1) \\$ $\dfrac{1}{2}(e^2-1)^2 \\$ $\dfrac{1}{2}(e^2-e) \\$ $\dfrac{1}{2}(e-\frac{1}{e})^2$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set4
calculus
definite-integrals
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 26
If $z$ is a complex variable, the value of $\displaystyle{} \int_{5}^{3i}\dfrac{dz}{z}$ is $− 0.511−1.57i$ $− 0.511+1.57i$ $0.511− 1.57i$ $0.511+1.57i$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set4
calculus
definite-integrals
complex-variables
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 2
The value of the integral $\int_{0}^{2}\dfrac{(x-1)^2\sin(x-1)}{(x-1)^2+\cos(x-1)}dx$ is $3$ $0$ $-1$ $-2$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set4
calculus
definite-integrals
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 26
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set1
calculus
definite-integrals
area-under-curve
0
answers
0
votes
GATE ME 2013 | Question: 47
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$ $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
piyag476
asked
in
Calculus
Feb 19, 2017
by
piyag476
1.4k
points
gateme-2013
calculus
definite-integrals
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