Find the area of the region bounded by the curves $y^2=9 x$ and $y=3 x$.

Find the area of the region bounded by the parabola $y^2=2 p x$ $x^2=2 p y$.

Find the area of the region bounded by the curve $y=x^3, y=x+6$ and $x=0$.

Find the area of the region bounded by the curve $y^2=4 x$ and $x^2=4 y$.

Find the area of the region included between $y^2=9 x$ and $y=x$.

Find the area of the region enclosed by the parabola $x^2=y$ and the line $y=x+2$.

Find the area of the region bounded by line $x=2$ and parabola $y^2=8 x$.

Sketch the region $\left\{(x, 0): y=\sqrt{4-x^2}\right\}$ and $X$-axis. Find the area of the region using integration.

Calculate the area under the curve $y=2 \sqrt{x}$ included between the lines $x=0$ and $x=1$.

Using integration, find the area of the region bounded by the line $2 y=5 x+7, X$-axis and the lines $x=2$ and $x=8$.

Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval $[1,5]$. Find the area under the curve and between the lines $x=1$ and $x=5$.

Determine the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$.

Find the area of the region bounded by $y=\sqrt{x}$ and $y=x$.

Find the area enclosed by the curve $y=-x^2$ and the straight line $x+y+2=0$.

Find the area bounded by the curve $y=\sqrt{x}, x=2 y+3$ in the first quadrant and $X$-axis.

Find the area of the region bounded by the curve $y^2=2 x$ and $x^2+y^2=4 x$.

Find the area bounded by the curve $y=\sin x$ between $x=0$ and $x=2 \pi$.

Find the area of region bounded by the triangle whose vertices are $(-1,1),(0,5)$ and $(3,2)$, using integration.

Draw a rough sketch of the region $\left\{(x, y): y^2 \leq 6 a x\right.$ and $\left.x^2+y^2 \leq 16 a^2\right\}$. Also, find the area of the region sketched using method of integration.

Compute the area bounded by the lines $x+2 y=2, y-x=1$ and $2 x+y=7$

Find the area bounded by the lines $y=4 x+5, y=5-x$ $4 y=x+5$.

Find the area bounded by the curve $y=2 \cos x$ and the $X$-axis from $x=0$ to $x=2 \pi$.

Draw a rough sketch of the given curve $y=1+|x+1|, x=-3, x=3$, $y=0$ and find the area of the region bounded by them, using integration.

The area of the region bounded by the $Y$-axis $y=\cos x$ and $y=\sin x$, where $0 \leq x \leq \frac{\pi}{2}$, is

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

The area of the region bounded by the curve $y=\sqrt{16-x^2}$ and $X$-axis is

Area of the region in the first quadrant enclosed by the $X$-axis, the line $y=x$ and the circle $x^2+y^2=32$ is

Area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is

The area of the region bounded by parabola $y^2=x$ and the straight line $2 y=x$ is

The area of the region bounded by the curve $y=\sin x$ between the ordinates $x=0, x=\frac{\pi}{2}$ and the $X$-axis is

The area of the region bounded by the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is

The area of the region bounded by the circle $x^2+y^2=1$ is

The area of the region bounded by the curve $y=x+1$ and the lines $x=2, x=3$, is

The area of the region bounded by the curve $x=2 y+3$ and the lines $y=1, y=-1$ is