Areas

Q. Let $I=c\int {\int }_{R}x{y}^{2}dxdy,$ where $R$ is the region shown in the figure and $c=6\times {10}^{-4}$ . The value of $I$ equals (Given the answer up to two decimal places).

1. 0.99

Q. The region specified by $\left\{\right(\rho ,\varphi ,z):3\le \rho \le 5,\frac{\pi }{8}\le \varphi \le \frac{\pi }{4},3\le z\le 4.5\}$ in cylindrical coordinates has volume of

1. 4.71

Q. The volume under the surface $z(x,y)=x+y$ and above the triangle in the $x-y$ plane defined by $0\le y\le xand0\le x\le 12$ is

1. 864

Q. A triangle in the $xy-$ plane is bounded by the straight lines $2x=3y,y=0$ and $x=3$. The volume above the triangle and under the plane $x+y+z=6$ is

1. 10

Q. The area include between the curve $y^2(2a-x)=x^3$ and its asymptote is

1. $3\pi a$
2. $3\pi a^2$
3. $4\pi a^2$
4. $6\pi a^2$

Q. The integral $\frac{1}{2\pi }\int {\int }_D(x+y+10)dxdy,$ where $D$ denotes the disc: $x^2+y^2\le 4,$ evaluates to

1. 20

Q. The integral $\frac{1}{2\pi }\int {\int }_D(x+y+10)dxdy,$ where $D$ denotes the disc: $x^2+y^2\le 4,$ evaluates to

1. 20