Integral of sqrt(1-x) dx

The solution

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  1             
  /             
 |              
 |    _______   
 |  \/ 1 - x  dx
 |              
/               
0

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

Integral(sqrt(1 - x), (x, 0, 1))

Detail solution

Let $u = 1 - x$ .

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:

$- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(1 - x)   
 | \/ 1 - x  dx = C - ------------
 |                         3      
/

$$\int \sqrt{1 - x}\, dx = C - \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2/3

$$\frac{2}{3}$$

2/3

$$\frac{2}{3}$$

2/3

Numerical answer [src]

0.666666666666667

0.666666666666667

The graph

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

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Integral of sqrt(1-x) dx

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The solution