Posted by **andy** on Thursday, July 25, 2013 at 2:11pm.

Evaluate ∬R 1/sqrt(x^2+y^2) dx dy, where R is the region bounded by y≥0 and x^2−x+y^2≤0.

- calculus -
**Steve**, Thursday, July 25, 2013 at 2:53pm
The region is the upper half of a circle with radius 1/2 centered at (1/2,0):

(x-1/2)^2 + y^2 = 1/4

So,

∫[0,1]∫[0,√1/4 - (x-1/2)^2) 1/√(x^2+y^2) dy dx

recall that √1/(x^2+y^2) dy = arcsinh(y/x) = log(x + √(x^2+y^2))

- calculus -
**Steve**, Thursday, July 25, 2013 at 2:54pm
oops that's log(y + √(x^2+y^2))

## Answer this Question

## Related Questions

- Calculus - Evaluate ∬R xy dA, where R is the region bounded by x^2+y^2&#...
- calculus - Let V be the volume of the region bounded by x^2+y^2≥z^2, z&#...
- calculus - Let V be the volume of the three-dimensional structure bounded by the...
- Calculus - Let V be the volume of the three-dimensional structure bounded by the...
- calculus (point me in the right direction please?) - Let V be the volume of the ...
- Calculus - Find the area of the region enclosed by y−2x^2 ≥ 0 and |...
- Calculus:) - Find the area of the region enclosed by y−2x^2≥0 and |x...
- Calculus:) - Find the area of the region enclosed by y−2x^2≥0 and |x...
- algebra - Identify the vertices of the solution region of the system of linear ...
- math - Maximize and minimize p = x + 2y subject to x + y ≥ 8 x + y ≤...