Find the area of the region bounded by the curve ay² = x³, the y-axis and the lines y= a and y = 2a.

Draw a rough sketch of the curve $y^2=8x$ and find the area of the region bounded by the curve $y^2=8x$ and the line $x=2$.

If the area of the region bounded by the line $2y=5x+7$, $x$-axis and the lines$x=2 \text{and} x=8$ is $k$ sq. units, then the value of $k$ is

Calculate the area under the curve $y=2\sqrt{x}$    included between the lines $x=0$ and $x=1$. Write the answer without unit.

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

Find the area bounded by the parabola $x=4-y^2$ and the $y-axis$.

The area of the region bounded by the parabola $y^2=4ax$ and its latus-rectum is $\frac{k}{3}{a}^2$ sq. units, then find the value of $k$.

The area of the region enclosed by the parabola $y^2=4ax$ and the chord $y=mx$ is $\frac{p{a}^2}{3m^3}$ sq.units, then the value of $p$.