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

Consider the region bounded by the lines $y - 1 = x, x = -2, x = 3$ and $x$ - axis. Then

(A) The area of the bounded region is given by $\int_{-2}^{3}(x + 1)dx$

(B) The numerical value of the area is $\frac{15}{2}$ sq. units

(C) The numerical value of the area is 8 sq. units

(D) The numerical value of the area is $\frac{17}{2}$ sq. units

Choose the correct answer from the options given below:

The area (in sq. units) of the region in the first quadrant enclosed between the line $x + y = 2$, parabola $y^2 = x$ and the x-axis, is

The area (in sq. units) bounded between the curves $x=e^y$, $x=e$ and x-axis in the first quadrant is

The supply function of a producer is given by $p = \frac{3}{5}e^{3x}$, where $x$ denotes a thousand units. If sales are 4000 units, then the producers' surplus is

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

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