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Solving integrals/ sqrt((12)^2+(36t)^2)

Integral of sqrt((12)^2+(36t)^2) dt

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                      
  /                      
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 |     _______________   
 |    /             2    
 |  \/  144 + (36*t)   dt
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0
$$\int\limits_{0}^{1} \sqrt{\left(36 t\right)^{2} + 144}\, dt$$ 
Integral(sqrt(144 + (36*t)^2), (t, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                            
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 |   /             2                                /        2 
 | \/  144 + (36*t)   dt = C + 2*asinh(3*t) + 6*t*\/  1 + 9*t  
 |                                                             
/
$$\int \sqrt{\left(36 t\right)^{2} + 144}\, dt = C + 6 t \sqrt{9 t^{2} + 1} + 2 \operatorname{asinh}{\left(3 t \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                 ____
2*asinh(3) + 6*\/ 10
$$2 \operatorname{asinh}{\left(3 \right)} + 6 \sqrt{10}$$ 
=
= 
                 ____
2*asinh(3) + 6*\/ 10
$$2 \operatorname{asinh}{\left(3 \right)} + 6 \sqrt{10}$$ 
2*asinh(3) + 6*sqrt(10)
Numerical answer [src] 
22.6105588794744
22.6105588794744

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

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