Mister Exam

Other calculators

x*sqrt(2-x)
Solving integrals/ x*sqrt(2-x)

Integral of x*sqrt(2-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |      _______   
 |  x*\/ 2 - x  dx
 |                
/                 
0
$$\int\limits_{0}^{1} x \sqrt{2 - x}\, dx$$ 
Integral(x*sqrt(2 - x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                
 |                               3/2            5/2
 |     _______          4*(2 - x)      2*(2 - x)   
 | x*\/ 2 - x  dx = C - ------------ + ------------
 |                           3              5      
/
$$\int x \sqrt{2 - x}\, dx = C + \frac{2 \left(2 - x\right)^{\frac{5}{2}}}{5} - \frac{4 \left(2 - x\right)^{\frac{3}{2}}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            ___
  14   16*\/ 2 
- -- + --------
  15      15
$$- \frac{14}{15} + \frac{16 \sqrt{2}}{15}$$ 
=
= 
            ___
  14   16*\/ 2 
- -- + --------
  15      15
$$- \frac{14}{15} + \frac{16 \sqrt{2}}{15}$$ 
-14/15 + 16*sqrt(2)/15
Numerical answer [src] 
0.575161133197968
0.575161133197968
The graph
Integral of x*sqrt(2-x) dx

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

    © Mister Exam – Calculator