Simple Quiz - Integration

Which one is correct for Gauss Divergence theorem?

• Surface Integral of the function is equal to the volume integral of the same function

• Line integral of the function is equal to the Surface integral of the function

• Surface integral of the function is equal to the Volume integral of the divergence of the function

• Line integral of the function is equal to the volume integral

Polar Coordinates of a hemisphere ?

• $x=\cos\theta,\ y=\sin\ \theta$

• $x=r,\ y=\theta$

• $x=y=\sin\theta$

• $x=r\cos\theta,\ y=r\sin\theta$

The line integral of the function over the curve is equal to the surface integral of the normal component of curl function over the surface.

Choose the correct theorem for this statement..

• Green's Theorem

• Stoke's theorem

• Gauss Divergence Theorem

 $y^2=x,\ y=x$  What are the points of intersections of the closed curves?

• (1.0 & (0,1))

• (0,0) & (2,2)

• (1,1) & (2,2)

• (0,0) & (1,1)

Choose the correct statement of Green's theorem

• $\int_{ }^{ }Pdx+Qdy=\int\int\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)dxdy$

• $\int_{ }^{ }Pdx+Qdy=\int_{ }^{ }\int_{ }^{ }\left(\frac{\partial P}{\partial y}-\frac{\partial Q}{\partial x}\right)dxdy$

• $\int_{ }^{ }Pdx+Qdy=\int_{ }^{ }\int_{ }^{ }\left(\frac{\partial P}{\partial y}+\frac{\partial Q}{\partial x}\right)dxdy$

• $\int_{ }^{ }Pdx-Qdy=\int_{ }^{ }\int_{ }^{ }\left(\frac{\partial P}{\partial y}-\frac{\partial Q}{\partial x}\right)dxdy$

dV=??, where V is the Volume of cube

• dx dy

• dy dz

• dx dy dz

• 0

Limit points of x and y for the surface $x^2+y^2=4$  

•  $x:\ -2\ to\ 2,\ y:\ 0\ to\ \sqrt{4-x^2}$  
  

•  $x:\ 0\ to\ 2,\ y:\ 0\ to\ \sqrt{4-x^2}$  
  

•  $x:\ 0\ to\ 2,\ y:\ -\sqrt{4-x^2}\ to\ \sqrt{4-x^2}$  
  

•  $x:\ -2\ to\ 2,\ y:\ -\sqrt{4-x^2}\ to\ \sqrt{4-x^2}$  

How many surfaces involves in the upper hemisphere?

• 3

• 1

• 2

• 4

Four points of a square OABC are (0,0), (a,0), (a,a) and (0,a), then the value of the function $x^2\overrightarrow{i}+yx\ \overrightarrow{j}$ along the line OA is ?? 

•  $yx\ \overrightarrow{j}$  

•  $x^2\overrightarrow{i}$  

•  $y$  

•  $x^2+1$