Mister Exam

Other calculators

y/sqrt(1+y^2)
Solving integrals/ y/sqrt(1+y^2)

Integral of y/sqrt(1+y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       y        
 |  ----------- dy
 |     ________   
 |    /      2    
 |  \/  1 + y     
 |                
/                 
0
∫01yy2+1 dy\int\limits_{0}^{1} \frac{y}{\sqrt{y^{2} + 1}}\, dy 
Integral(y/sqrt(1 + y^2), (y, 0, 1))
Detail solution

  1. Let u=y2+1u = \sqrt{y^{2} + 1}.

    Then let du=ydyy2+1du = \frac{y dy}{\sqrt{y^{2} + 1}} and substitute dudu:

    ∫1 du\int 1\, du

    1. The integral of a constant is the constant times the variable of integration:

      ∫1 du=u\int 1\, du = u

    Now substitute uu back in:

    y2+1\sqrt{y^{2} + 1}

  2. Add the constant of integration:

    y2+1+constant\sqrt{y^{2} + 1}+ \mathrm{constant}

The answer is:

y2+1+constant\sqrt{y^{2} + 1}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                
 |                         ________
 |      y                 /      2 
 | ----------- dy = C + \/  1 + y  
 |    ________                     
 |   /      2                      
 | \/  1 + y                       
 |                                 
/
∫yy2+1 dy=C+y2+1\int \frac{y}{\sqrt{y^{2} + 1}}\, dy = C + \sqrt{y^{2} + 1}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
       ___
-1 + \/ 2
−1+2-1 + \sqrt{2} 
=
= 
       ___
-1 + \/ 2
−1+2-1 + \sqrt{2} 
-1 + sqrt(2)
Numerical answer [src] 
0.414213562373095
0.414213562373095
The graph
Integral of y/sqrt(1+y^2) dy

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

    © Mister Exam – Calculator