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Recent questions tagged definite-integral

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GATE Civil 2021 Set 2 | Question: 18
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
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GATE2017 CE-2-27
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is$\dfrac{\pi ^3}{24} \\$$\dfr...
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GATE2016-2-29
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
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GATE2016-1-27
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is $\dfrac{\pi}{2} \\$ $\pi \\$ $\dfrac{3 \pi}{2} \\$ $1$
The value of $\int_0^{\infty} \dfrac{1}{1+x^2} dx + \int _0^{\infty} \dfrac{\sin x}{x} dx$ is$\dfrac{\pi}{2} \\$$\pi \\$$\dfrac{3 \pi}{2} \\$$1$
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GATE2016-1-28
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is $\dfrac{59}{6} \\$ $\dfrac{9}{2} \\$ $\dfrac{10}{3} \\$ $\dfrac{7}{6}$
The area of the region bounded by the parabola $y=x^2+1$ and the straight line $x+y=3$ is$\dfrac{59}{6} \\$$\dfrac{9}{2} \\$$\dfrac{10}{3} \\$$\dfrac{7}{6}$
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GATE2015-2-3
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is: $1$ $-1$ $i$ $-i$
Given, $i=\sqrt{-1}$, the value of the definite integral, $I= \int_0^{\pi/2} \dfrac{\cos x+ i \sin x}{\cos x – i \sin x} dx$ is:$1$$-1$$i$$-i$
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GATE Civil 2013 | Question: 28
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is $0 \\$ $\dfrac{1}{15} \\$ $1 \\$ $\dfrac{8}{3}$
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is$0 \\$$\dfrac{1}{15} \\$$1 \\$$\dfrac{8}{3}$
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GATE2018 CE-1: 26
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is $\pi^2/8$ $\pi^2/4$ $\pi^2/2$ $\pi^2$
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is$\pi^2/8$$\pi^2/4$$\pi^2/2$$\pi^2$
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