Area Under Curves

The area (in sq. units) of the part of circle $x^{2}+y^{2}=169$which is below the line $5x-y=13$ is $\frac{\pi\,\alpha\,}{2\beta\,}-\frac{65}{2}+\frac{\alpha\,}{\beta\,}\sin\,^{-1}\left(\frac{12}{13}\right)$ where…

If the area bounded by the curve $2y^{2}=3x$, lines $x+y=3,y=0$ and outside the circle $\left(x-3\right)^{2}+y^{2}=2$ is A, then $4\left(\pi\,+4A\right)$ is equal to __________.

The area (in sq. units) of the region enclosed between the parabola $y^{2}=2x$and the line $x+y=4$is ______?

Let $A=\left{\left(x,y\right):y^{2}\leq\,4x,y-2x\geq\,-4\right}$. The area of the region$A$in square unitsis

The area of the region enclosed by the parabola $(y-2)^{2}=x-1$, the line $x-2y+4=0$and the positive coordinate axes is __________?

Let $\alpha\,$be the area of the larger region bounded by the curve $y^{2}=8x$ and the lines $y=x$ and $x=2$, which lies in the first quadrant. Then the value of $3\alpha\,$ is equal to

Let…

The area of the region given by $A=\left\{\left(x,y\right):x^{2}\leq\,y\leq\,\min\,\left\{x+2,4-3x\right\}\right\}$ is

Let the area enclosed by the lines $x+y=2,y=0$, $x=0$and the curve $f(x)=\min\,\left{x^{2}+\frac{3}{4},1+[x]\right}$ where $[x]$ denotes the greatest integer $\leq\,x$, be $A$. Then the value of $12A$ is

If the line $y=mx$ bisects the area enclosed by the lines $x=0,y=0,x=\frac{3}{2}$ and the curve $y=1+4x-x^{2},$then $12m$ is equal to .

Let the area of the region ${(x,y):x-2y+4\geq\,0, \leftx+2y^{2}\geq\,0,x+4y^{2}\leq\,8,y\geq\,0\right}$ be $\frac{m}{n}$, where $m$ and $n$ are coprime numbers. Then $m+n$ is equal to ______.

The area enclosed by the curves $y=\log\,_{e}\left(x+e^{2}\right),x=\log\,_{e}\left(\frac{2}{y}\right)$and $x=\log\,_{e}2$, above the line $y=1$is