Area bounded by the curves $y = 3^x, y = x$ and $x = 1, x = 2$ is:

The area bounded by the curve $y = 4 + 3x - x^2$ and $x$-axis is equal to

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

The area of the region bounded by parabola $x^2 = 4y$, straight line $x = 2$ and $x$-axis, is

The area (in sq. units) of the region bounded by the curve $x^2 = 250y$, $y = 0$ and $x = 50$ 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:

If the supply curve is $p = \sqrt{9+x}$ and the quantity sold in market is 7 units, then the producer's surplus will be