Integral of sqrt(x+4) dx

The solution

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  1             
  /             
 |              
 |    _______   
 |  \/ x + 4  dx
 |              
/               
0

$$\int\limits_{0}^{1} \sqrt{x + 4}\, dx$$

Integral(sqrt(x + 4), (x, 0, 1))

Detail solution

Let $u = x + 4$ .

Then let $du = dx$ and substitute $du$ :

$\int \sqrt{u}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

$\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(x + 4)   
 | \/ x + 4  dx = C + ------------
 |                         3      
/

$$\int \sqrt{x + 4}\, dx = C + \frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

            ___
  16   10*\/ 5 
- -- + --------
  3       3

$$- \frac{16}{3} + \frac{10 \sqrt{5}}{3}$$

            ___
  16   10*\/ 5 
- -- + --------
  3       3

$$- \frac{16}{3} + \frac{10 \sqrt{5}}{3}$$

-16/3 + 10*sqrt(5)/3

Numerical answer [src]

2.12022659166597

2.12022659166597

The graph

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

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Integral of sqrt(x+4) dx

Limits of integration:

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Piecewise:

The solution