Test: Multiple Integrals - Mathematics MCQ

The volume of an object expressed in spherical co-ordinates is given by

The value of the integral is

Changing the order of the integration in the double integral
 What is q? 

By a  change of variable x(u,v) = uv, y(u,v) = v/u is double integral, the integrand f(x,y) change to f(uv, v/u) φ (u,v). Then φ (u,v) is 

The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of 

Consider the shaded triangular region P shown in the figure. What is 

the parabolic arc  is revolved around the x-axis. The volume of

A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x+y)² on path AB traversed in a counterclockwise sense is 
 

What is the area common to the circles r = a and r = 2a cos θ? 

The value of  (6 − x− y) dx dy = 0 

A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is  where x is the horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

The expression  for the volume of a cone is equal to  

 A surface s(x,y) = 2x + 5y - 3 is integrated once over a path consisting of the points that satisfy (x+1)2 + (y-1)2 = √2. The integral evaluates to

f ( x,y ) is a continuous defined over ( x,y ) ∈ [0,1]× [0,1] . Given two constrains,x > y² and y > x² , the volume under f ( x,y ) is 

The value fo integral  dx dy is