Integral of sqrt(-x) dx

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  0          
  /          
 |           
 |    ____   
 |  \/ -x  dx
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-4

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

Integral(sqrt(-x), (x, -4, 0))

Detail solution

Let $u = - x$ .

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

$\int \left(- \sqrt{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt{u}\, du = - \int \sqrt{u}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
  So, the result is: $- \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                         
 |                       3/2
 |   ____          2*(-x)   
 | \/ -x  dx = C - ---------
 |                     3    
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3

$$\frac{16}{3}$$

16/3

$$\frac{16}{3}$$

16/3

Numerical answer [src]

5.33333333333333

5.33333333333333

The graph

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