Test: Multiple Integrals - Mathematics MCQ
17 Questions MCQ Test - Test: Multiple Integrals
A triangle ABC consists of vertex points A (0,0) B(1,0) and C(0,1). The value of the integral ∫∫ 2x dxdy over the triangle is
sin (x+y)dx dy is
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The area enclosed between the parabala y = x2 and the straight line y = x is
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?
(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
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
dx dy is 
Important Questions for Multiple Integrals
Multiple Integrals MCQs with Answers
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