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Solving integrals/ sqrt(xy-y^2)

Integral of sqrt(xy-y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  x*y - y   dy
 |                  
/                   
0
∫01xy−y2 dy\int\limits_{0}^{1} \sqrt{x y - y^{2}}\, dy
Simplify
The answer [src] 
                        2    /               ________\      2       
  ________ /1   x\   I*x *log\-2 + x + 2*I*\/ -1 + x /   I*x *log(x)
\/ -1 + x *|- - -| - --------------------------------- + -----------
           \2   4/                   8                        8
ix2log⁡(x)8−ix2log⁡(x+2ix−1−2)8+(−x4+12)x−1\frac{i x^{2} \log{\left(x \right)}}{8} - \frac{i x^{2} \log{\left(x + 2 i \sqrt{x - 1} - 2 \right)}}{8} + \left(- \frac{x}{4} + \frac{1}{2}\right) \sqrt{x - 1} 
=
= 
                        2    /               ________\      2       
  ________ /1   x\   I*x *log\-2 + x + 2*I*\/ -1 + x /   I*x *log(x)
\/ -1 + x *|- - -| - --------------------------------- + -----------
           \2   4/                   8                        8
ix2log⁡(x)8−ix2log⁡(x+2ix−1−2)8+(−x4+12)x−1\frac{i x^{2} \log{\left(x \right)}}{8} - \frac{i x^{2} \log{\left(x + 2 i \sqrt{x - 1} - 2 \right)}}{8} + \left(- \frac{x}{4} + \frac{1}{2}\right) \sqrt{x - 1}
Simplify

    Use the examples entering the upper and lower limits of integration.

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