Doc - MCQ:- Calculus, Integrals, Multiple, integrals | Topic-wise Tests & Solved Examples for Mathematics PDF Download

Question:-1
Solution:  Region bounded  by
x = 0, x = 1 and y = x, y = 1
Now we evaluate the integral by hanging the order of integral

Question:-2 The value of the double integral
Solution:  Region of integration is bounded  y=0, y = x and x = 0, x = π
 changing the order of integration


= 2

Question:-3 Evaluate
Solution: 

Question4:- Change the order of integration in the double integral
Solution:  Domain of integration is bounded  by the following curves

point of intersection of the curve y =2 - x² and y = -x we get when

So (-1,1 ) and (2,-2 ) are the points of intersection.
Now the given integral modify by changing the order of integration we get

Something skip follow book

 Question5:- Changing the order of integration of




Solution:
The region of integration is bounded by y = 0, y = x, x = 1, x = 2 after changing the order the integration changes to

Question6:- Let D the trianle bounded by the y-axis the line 2y = π. Then the value of the integral
(a) 1/2 (b) 1 (c) 3/2 (d) 2
Solution: 

Question7:- Change the order of integration in the integral
Solution:  The domain of the double integration is bounded  by the curves y = x - 1,

Question8:- Let I =   Then using the transformation x = rcosθ, y = rsinθ, integral is equal to




Solution:  Region of integration is bounded  by curves

for first integral,

Question9:- Evaluate integral
(a) 0 (b) 1/2 (c) 1 (d)2
Solution:  Region of integration is bounded  by curves

 changing the order

Question 10:- The value of  equals
(a) π/4 (b) 1/2π (c) 1/4 (d) 1/2
Solution:

Question11:- (a) Find in the area of the smaller of the two regions enclose between

Solution:- 

Solution (b)
The region of integration is bounded  by x = 0, x = y, y = 1, y = ∞ and shown in figure changing the order


Question12:- Let f , be a continuous function with
Solution:  Given,  be a continuous function with

 Now apply change of order of integration
 Domain of integration is given by graph

Question13:- By changing the order of integration, the integral  can be expressed as




Solution:  The domain of integration is bounded  y = 1,   changing the order