Please help Calculate the iterated integral (double)

Question

₀∫²(₀∫^¶/2 xsin(y)dy)dx

Answer 1

 
  First solve integral from 0 to ¶/2 of the sin(y)dy
 

      Solution is =>-cos¶/2-(-cos 0)=0 + 1 = 1

 

Now double integral looks

 

 
 ∫ x*1dx

 

Solution is =>  (x^2)/2  from 0 to 2

                        (2^2)/2 - (0^2)/2 = 2-0=2

 

Final solution and the answer to the problem is 2

Answer 2

This shows up as
0∫2(0∫¶/2 xsin(y)dy)dx    in the problem listing and as

0∫²(0∫^¶/2 xsin(y)dy)dx    in the problem description.  The ¶ makes no since.

If what you mean is

₀∫²(₀∫^pi/2 xsin(y)dy)dx 

(since the answers has poor capabilities for math symbols)

then the answer is

definite integral = 2

indefinite integral = x²/2 + constant