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Test: Multiple Integrals - Mathematics MCQ


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17 Questions MCQ Test Calculus - Test: Multiple Integrals

Test: Multiple Integrals for Mathematics 2024 is part of Calculus preparation. The Test: Multiple Integrals questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Multiple Integrals MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Multiple Integrals below.
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Test: Multiple Integrals - Question 1

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 

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Test: Multiple Integrals - Question 2

 sin (x+y)dx dy is

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Test: Multiple Integrals - Question 3

The area enclosed between the parabala y = x and the straight line y = x is 

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Test: Multiple Integrals - Question 4

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

The value of the integral is

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Test: Multiple Integrals - Question 5

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

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When 

i.e.

Now 

Test: Multiple Integrals - Question 6

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 

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Test: Multiple Integrals - Question 7

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

Test: Multiple Integrals - Question 8

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

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The equation of the line AB

Test: Multiple Integrals - Question 9

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

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Differential volume
dv = πy2dy
Volume from x = 1 to x = 2

Test: Multiple Integrals - Question 10

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 
 

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Test: Multiple Integrals - Question 11

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

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Area common to circles r = a 
And r = 2a cos θ is 1.228 a2

Test: Multiple Integrals - Question 12

The value of  (6 − x− y) dx dy = 0 

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Test: Multiple Integrals - Question 13

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

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We know length of the curve f(x) between x = a and x = b given by

Test: Multiple Integrals - Question 14

The expression  for the volume of a cone is equal to  

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Choices (a) and (d) can be correct because variable is r in these two.
By integrating (d), we get 1/3πr2H, which is volume of cone.

Test: Multiple Integrals - Question 15

 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

Test: Multiple Integrals - Question 16

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 

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Test: Multiple Integrals - Question 17

The value fo integral  dx dy is  

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