Cartesian coordinates->; Polar coordinates are

[double integer symbol] f(x, y)dxdy? =? [double integer symbol] f(rcosA, rsinA)*rdrdA.

Where x=rcosA,? y=rsinA。

The original title was originally (integer abbreviation [product (upper limit, lower limit)])

[product (a, 0)]dx[ product (x, 0)] (x 2+y 2) (1/2) dy

After substitution, the xy coordinates are expressed by the distance from the origin to the X axis and the counterclockwise angle respectively. Or by calculating the definite integral twice.

This problem is to divide the plane into several strips according to the angle, and then integrate the strips first and then the angle. R ranges from 0 to acos(θ), and θ ranges from 0 to π/4.

If you need detailed information, read the advanced mathematics book of Tongji edition. It's good.

I hope I made myself clear to you.