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Identical expressions
sqrt(three -2s)ds
square root of (3 minus 2s)ds
square root of (three minus 2s)ds
√(3-2s)ds
sqrt3-2sds
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sqrt(3+2s)ds

Integral of sqrt(3-2s)ds dx

The solution

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  1               
  /               
 |                
 |    _________   
 |  \/ 3 - 2*s  ds
 |                
/                 
0

$$\int\limits_{0}^{1} \sqrt{3 - 2 s}\, ds$$

Integral(sqrt(3 - 2*s), (s, 0, 1))

Detail solution

Let $u = 3 - 2 s$ .

Then let $du = - 2 ds$ and substitute $- \frac{du}{2}$ :

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                               3/2
 |   _________          (3 - 2*s)   
 | \/ 3 - 2*s  ds = C - ------------
 |                           3      
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1     ___
- - + \/ 3 
  3

$$- \frac{1}{3} + \sqrt{3}$$

  1     ___
- - + \/ 3 
  3

$$- \frac{1}{3} + \sqrt{3}$$

-1/3 + sqrt(3)

Numerical answer [src]

1.39871747423554

1.39871747423554

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

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Integral of sqrt(3-2s)ds dx

Limits of integration:

The graph:

Piecewise:

The solution