# Question:a very strange problem with double integral

## Question:a very strange problem with double integral

Maple 14
`I am just a Newbie. Today I calculated a double integral using Maple 14 for linux amd64, but the results are  so strange that I think there must be something wrong.  I using two methods, the first is by using int(int(Integrand, inner variable), outer variable), the second is by calculating the inner integral first, then calculating the outer integral step by step.  But the two result are different.  Here is my codes: `
`restart;assume(a>0):Int(Int(rho^2,rho=0..a*csc(theta)),theta=Pi/4..Pi/2);             /1/2 Pi   /a csc(theta)                             |         |                 2                        |         |              rho  drho dtheta            |         |                                         /1/4 Pi   /0                              value(%);        1  3  (1/2)   1   3         1  3   /     (1/2)\        - a  2      - -- a  ln(2) + - a  ln\2 + 2     /        6             12            6                  int(rho^2,rho=0..a*csc(theta));                        1  3           3                        - a  csc(theta)                         3               int((3),theta);          3                                                       a  cos(theta)   1  3                                   - ------------- + - a  ln(csc(theta) - cot(theta))                     2   6                                        6 sin(theta)                                    g:=theta->(4);            3                                                         a  cos(theta)   1  3                            theta -> - ------------- + - a  ln(csc(theta) - cot(theta))                       2   6                                          6 sin(theta)                                    g(Pi/2)-g(Pi/4);               1  3  (1/2)   1  3   / (1/2)    \               - a  2      - - a  ln\2      - 1/               6             6                  (6)-(2);     1  3   / (1/2)    \   1   3         1  3   /     (1/2)\   - - a  ln\2      - 1/ + -- a  ln(2) - - a  ln\2 + 2     /`
`     6                     12            6      `
` `
`Can anyone tell me what is the reason for this difference? Many thanks!            `
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