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Recent questions tagged definite-integral

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GATE Electrical 2020 | Question: 2
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ ...

go_editor asked in Calculus Feb 28, 2020

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GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).

Arjun asked in Calculus Feb 19, 2018

by Arjun

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3

GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).

Arjun asked in Calculus Feb 19, 2018

by Arjun

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4

GATE Electrical 2014 Set 2 | Question: 26
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\dfrac{2x-y}{2} \bigg)$ and $v=\dfrac{y}{2}$ ... $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}u \: du \bigg ) dv$

makhdoom ghaya asked in Calculus Feb 12, 2017

by makhdoom ghaya

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5

GATE Electrical 2016 Set 2 | Question: 29
The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to $0$ $0.5$ $1$ $2$

makhdoom ghaya asked in Calculus Jan 30, 2017

by makhdoom ghaya

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6

GATE Electrical 2016 Set 1 | Question: 9
The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is $\dfrac{1}{2e} \\$ $\dfrac{2}{e} \\$ $\dfrac{1}{e^{2}} \\$ $\dfrac{1}{2e^{2}}$

makhdoom ghaya asked in Calculus Jan 30, 2017

by makhdoom ghaya

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7

GATE Electrical 2016 Set 1 | Question: 5
The value of the integral $\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$ over the contour $\mid z \mid=1$, taken in the anti-clockwise direction, would be $\dfrac{24 \pi i}{13} \\$ $\dfrac{48 \pi i}{13} \\$ $\dfrac{24}{13} \\$ $\dfrac{12}{13}$

makhdoom ghaya asked in Calculus Jan 30, 2017

by makhdoom ghaya

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