Doc - MCQ:- Calculus, Integrals, Multiple, integrals

Que 1:

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

Que 2: The value of the double integral

Sol:  Region of integration is bounded  y=0, y = x and x = 0, x = π
 changing the order of integration


= 2

Que :-3 Evaluate

Sol: 

Que 4:- Change the order of integration in the double integral

Sol:  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

 Que 5:- Changing the order of integration of

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

Que 6:- Let D the triangle 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

Sol: 

Que 7: Change the order of integration in the integral

Sol:

Que 8:- Let I =  Then using the transformation x = rcosθ, y = rsinθ, integral is equal to

Sol: 

Que 9: Evaluate integral
(a) 0 
(b) 1/2 
(c) 1 
(d)2

Sol:  Region of integration is bounded  by curves

 changing the order

Que10:- The value of  equals
(a) π/4 
(b) 1/2π 
(c) 1/4 
(d) 1/2
Sol:

Que 11:
(a) Find in the area of the smaller of the two regions enclose between

Sol: 

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

Que12:- Let f , be a continuous function with

Sol:  

Que13:- By changing the order of integration, the integral  can be expressed as

Sol: