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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 $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$
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}$$\pi$
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GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$
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GATE ME 2012 | Question: 11
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is $1/6$ $1/4$ $1/3$ $1/2$
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is$1/6$$1/4$$1/3$$1/2$
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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 = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
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 = $...
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GATE Mechanical 2014 Set 4 | Question: 27
The value of the integral $\int_{0}^{2}\int_{0}^{x}e^{x+y}dydx$ is $\dfrac{1}{2}(e-1) \\$ $\dfrac{1}{2}(e^2-1)^2 \\$ $\dfrac{1}{2}(e^2-e) \\$ $\dfrac{1}{2}(e-\frac{1}{e})^2$
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$
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GATE Mechanical 2014 Set 4 | Question: 26
If $z$ is a complex variable, the value of $\displaystyle{} \int_{5}^{3i}\dfrac{dz}{z}$ is $− 0.511−1.57i$ $− 0.511+1.57i$ $0.511− 1.57i$ $0.511+1.57i$
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$$0.511+1.57i$
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GATE Mechanical 2014 Set 4 | Question: 2
The value of the integral $\int_{0}^{2}\dfrac{(x-1)^2\sin(x-1)}{(x-1)^2+\cos(x-1)}dx$ is $3$ $0$ $-1$ $-2$
The value of the integral $$\int_{0}^{2}\dfrac{(x-1)^2\sin(x-1)}{(x-1)^2+\cos(x-1)}dx$$ is$3$$0$$-1$$-2$
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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 $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
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$$\frac{-\p...
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GATE ME 2013 | Question: 47
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$ $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is$\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$$\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$$\dfrac{2}{9}\sqrt{e^3...
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