Area of the region bounded by $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ 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:

Evaluate $\int_0^{\frac{1}{3}} y \, dx$

The area of the region (in square units) bounded by $x=1, x=2$ and the curve $y^2 = 4x$ in the first quadrant is

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

The area (in sq. units) of the bigger portion of region enclosed by the curves $4x^2 + 9y^2 = 36$ and $2x + 3y = 6$ is

Area (in sq. units) of the region bounded by curves $y^2 = x$ and $x = 4$ is