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sqrt(2-x)

Integral of sqrt(2-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |    _______   
 |  \/ 2 - x  dx
 |              
/               
0               
$$\int\limits_{0}^{1} \sqrt{2 - x}\, dx$$
Integral(sqrt(2 - x), (x, 0, 1))
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. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                             3/2
 |   _______          2*(2 - x)   
 | \/ 2 - x  dx = C - ------------
 |                         3      
/                                 
$$\int \sqrt{2 - x}\, dx = C - \frac{2 \left(2 - x\right)^{\frac{3}{2}}}{3}$$
The graph
The answer [src]
          ___
  2   4*\/ 2 
- - + -------
  3      3   
$$- \frac{2}{3} + \frac{4 \sqrt{2}}{3}$$
=
=
          ___
  2   4*\/ 2 
- - + -------
  3      3   
$$- \frac{2}{3} + \frac{4 \sqrt{2}}{3}$$
-2/3 + 4*sqrt(2)/3
Numerical answer [src]
1.21895141649746
1.21895141649746
The graph
Integral of sqrt(2-x) dx

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