The area of the region bounded by curves $y = |x-4|$, $x = 1$, $x = 5$ and the x-axis is

The smaller area enclosed by the curve $y = |x|$ and the circle $(x-a)^2 + y^2 = a^2$ is:

The area of the region bounded by the parabola $y^2 = 8x$ and its latus rectum in the first quadrant, is

The area of the region bounded by the lines $x+2 y=12, x=2, x=6$ and $x$-axis is :

$y(x)$ is strictly increasing in the interval

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 bounded by the curve $y^2 = 2x$ and the lines $y = 2, y = 4$ and y-axis, is