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

The area of the region bounded by $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is $\frac{m}{n}$ sq. units, where $\gcd(m, n) = 1$, then $m - n$ is equal to:

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 bounded by the curve $y = 2x^3$, $x$ - axis and ordinates $x = -1$ and $x = 1$ is:

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

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

The area (in sq. units) of the region bounded by $y = 2\sqrt{1 - x^2}$, $x \in [0, 1]$ and $x$-axis is equal to