Mister Exam

Other calculators

Solving integrals/ sqrt(x^2+y^2)

Integral of sqrt(x^2+y^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     _________   
 |    /  2    2    
 |  \/  x  + y   dx
 |                 
/                  
0
∫01x2+y2 dx\int\limits_{0}^{1} \sqrt{x^{2} + y^{2}}\, dx 
Integral(sqrt(x^2 + y^2), (x, 0, 1))
The answer (Indefinite) [src] 
                                                 ________
                                                /      2 
  /                                            /      x  
 |                        2      /x\   x*y*   /   1 + -- 
 |    _________          y *asinh|-|         /         2 
 |   /  2    2                   \y/       \/         y  
 | \/  x  + y   dx = C + ----------- + ------------------
 |                            2                2         
/
∫x2+y2 dx=C+xyx2y2+12+y2asinh⁡(xy)2\int \sqrt{x^{2} + y^{2}}\, dx = C + \frac{x y \sqrt{\frac{x^{2}}{y^{2}} + 1}}{2} + \frac{y^{2} \operatorname{asinh}{\left(\frac{x}{y} \right)}}{2}
Simplify

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

    © Mister Exam – Calculator