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Solving integrals/ sqrt((kx(2l-x))\m)

Integral of sqrt((kx(2l-x))\m) dt

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  t                       
  /                       
 |                        
 |      _______________   
 |     / k*x*(2*l - x)    
 |    /  -------------  dt
 |  \/         m          
 |                        
/                         
0
$$\int\limits_{0}^{t} \sqrt{\frac{k x \left(2 l - x\right)}{m}}\, dt$$
Simplify
Detail solution

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

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 |     _______________                _______________
 |    / k*x*(2*l - x)                / k*x*(2*l - x) 
 |   /  -------------  dt = C + t*  /  ------------- 
 | \/         m                   \/         m       
 |                                                   
/
$$t\,\sqrt{{{k\,\left(2\,l-x\right)\,x}\over{m}}}$$
Simplify
The answer [src] 
      ________________
     / k*x*(-x + 2*l) 
t*  /  -------------- 
  \/         m
$$t\,\sqrt{{{k\,\left(2\,l-x\right)\,x}\over{m}}}$$ 
=
= 
      ________________
     / k*x*(-x + 2*l) 
t*  /  -------------- 
  \/         m
$$t \sqrt{\frac{k x \left(2 l - x\right)}{m}}$$
Simplify

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

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