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Integral of sqrt(3x+4) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  0               
  /               
 |                
 |    _________   
 |  \/ 3*x + 4  dx
 |                
/                 
4                 
$$\int\limits_{4}^{0} \sqrt{3 x + 4}\, dx$$
Integral(sqrt(3*x + 4), (x, 4, 0))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                                 3/2
 |   _________          2*(3*x + 4)   
 | \/ 3*x + 4  dx = C + --------------
 |                            9       
/                                     
$$\int \sqrt{3 x + 4}\, dx = C + \frac{2 \left(3 x + 4\right)^{\frac{3}{2}}}{9}$$
The graph
The answer [src]
-112/9
$$- \frac{112}{9}$$
=
=
-112/9
$$- \frac{112}{9}$$
-112/9
Numerical answer [src]
-12.4444444444444
-12.4444444444444

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