- #1
kingwinner
- 1,270
- 0
I find this to be a very tough problem:
1) Determine whether the improper integral I
∞ ∞
∫ ∫ [sin (x2 + y2) / ln(x2 + y2)] dxdy
2 2
converges or diverges.
All I can think of and try is by changing it to polar coordinates:
I=A+B where
A=
pi/4--- ∞
∫ ----- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)
2 -- 2/sin(theta)
B=
pi/2 -------∞
∫---------- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)
pi/4 ---2/cos(theta)
But how can I show that each of them converges (or diverges)?
Can someone please help me out? Thank you!
1) Determine whether the improper integral I
∞ ∞
∫ ∫ [sin (x2 + y2) / ln(x2 + y2)] dxdy
2 2
converges or diverges.
All I can think of and try is by changing it to polar coordinates:
I=A+B where
A=
pi/4--- ∞
∫ ----- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)
2 -- 2/sin(theta)
B=
pi/2 -------∞
∫---------- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)
pi/4 ---2/cos(theta)
But how can I show that each of them converges (or diverges)?
Can someone please help me out? Thank you!