The area bounded by the curve $y^2 = 2x$, $y$-axis and the line $y=1$, is

The area (in sq. units) bounded by the parabola $y^2 = x$ and line $x = 4$ in first quadrant is equal to $A$, then which of the following statements is/are TRUE ?

A. $A = \dfrac{16}{3}$

B. $A = \displaystyle\int_0^4 \sqrt{x}\, dx$

C. $A = 2\displaystyle\int_0^4 \sqrt{x}\, dx$

D. $A = \displaystyle\int_0^2 y^2\, dy$

Choose the correct answer from the options given below:

The area (in sq.units) bounded by the lines $y=2x+3$, $y=0$ between $x=-2$ and $x=1$ is

The area bounded by the curve $y = \log x, y = 0$ and $x = e$, is

The area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum is:

If the area(in square units) bounded by the curves $y^2 = 4x$ and $y = x$ is $\dfrac{k^3}{3}$, then the value of $k$ is:

The area in the first quadrant bounded by $y = 9x^2$, $x = 0$, $y = 1$ and $y = 4$ is :