# GATE2015-3-41

The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
in Calculus
recategorized

## Related questions

The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ and ${\overline{r}}'$ ... $\hat{j}$ are the basis vectors in the $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
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The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\Gamma$ is