Area Bounded between Two Curves

The area (in sq. units) bounded by the parabola $y=x^2+3,$ the tangent to the parabola at $(3,12)$ and the coordinate axes which is lying in the first quadrant is

The area (in sq. units) bounded by the parabola $y=x^2-1$ the tangent at the point $\left(2, 3\right)$ to it and the

$y–$ axis is:

The area enclosed between the curves $y^2=x$ and $y=\left|x\right|$ is

The area of the region bounded by $x=0,y=0,x=2,y=2,y\le e^x$ and $y\ge \ln x$ is

The area bounded by the curves $y=\sqrt{x},$ $2y+3=x$ and $x$-axis in the $1^{\mathrm{st}}$ quadrant is

The area (in sq. unit) of the region bounded by the curve $y=x\left|x\right|$ , $x-$ axis and the ordinates $x=1,\mathrm{ }x=-1$ is given by

The area bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is

The area enclosed by the parabola $y^2=4ax$ and the straight line $y=2ax,$ is

The area between the curve $y^2=4ax,$ $x-$ axis and the ordinates $x=0$ and $x=a$ is

The area of the region bounded by $y=\left|x-1\right|$ and $y=1$ is

Area bounded by the parabola $y^2=4ax$ and its latus rectum is

The area bounded by the circle $x^2+y^2=4$, line $x=\sqrt{3}y$ and $x$-axis lying in the first quadrant, is

If the area above the $x-$axis, bounded by the curves $y=2^{kx}$, $x=0$ and $x=2$ is $\frac{3}{\mathrm{l}\mathrm{n}\mathrm{ }2}$, then the value of $k$ is

For $0\le x\le \pi ,$ the area bounded by $y=x$ and $y=x+\sin x,$ is

Area bounded by parabola $y^2=x$ and straight line $2y=x$ is

If area bounded by the curves $y^2=4ax$ and $y=mx$ is $\frac{a^2}{3}$, then the value of $m$ is

The area enclosed between the parabola $y=x^2-x+2$ and the line $y=x+2$ (in square unit) is equal to

Let $f\left(x\right)=$ Maximum $\left\{x^2,{\left(1-x\right)}^2, 2x\left(1-x\right)\right\}$, where $0\le x\le 1.$ Determine the area of the region bounded by the curves $y=f\left(x\right)$, $x$-axis, $x=0 \& x=1$