Mister Exam

Other calculators

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

Integral of sqrt(x)*exp(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 1/5            
  /             
 |              
 |    ___  -x   
 |  \/ x *e   dx
 |              
/               
0
∫015xe−x dx\int\limits_{0}^{\frac{1}{5}} \sqrt{x} e^{- x}\, dx 
Integral(sqrt(x)*exp(-x), (x, 0, 1/5))
Detail solution

    UpperGammaRule(a=-1, e=1/2, context=sqrt(x)*exp(-x), symbol=x)

  1. Add the constant of integration:

    −xe−x−πerfc⁡(x)2+constant- \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}+ \mathrm{constant}

The answer is:

−xe−x−πerfc⁡(x)2+constant- \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                 
 |                                  ____     /  ___\
 |   ___  -x            ___  -x   \/ pi *erfc\\/ x /
 | \/ x *e   dx = C - \/ x *e   - ------------------
 |                                        2         
/
∫xe−x dx=C−xe−x−πerfc⁡(x)2\int \sqrt{x} e^{- x}\, dx = C - \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}
Simplify
The graph
0.000.200.020.040.060.080.100.120.140.160.180.00.5
Plot the graph f(x)
The answer [src] 
          /  ___\              
  ____    |\/ 5 |              
\/ pi *erf|-----|     ___  -1/5
          \  5  /   \/ 5 *e    
----------------- - -----------
        2                5
−55e15+πerf⁡(55)2- \frac{\sqrt{5}}{5 e^{\frac{1}{5}}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5}}{5} \right)}}{2} 
=
= 
          /  ___\              
  ____    |\/ 5 |              
\/ pi *erf|-----|     ___  -1/5
          \  5  /   \/ 5 *e    
----------------- - -----------
        2                5
−55e15+πerf⁡(55)2- \frac{\sqrt{5}}{5 e^{\frac{1}{5}}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5}}{5} \right)}}{2} 
sqrt(pi)*erf(sqrt(5)/5)/2 - sqrt(5)*exp(-1/5)/5
Numerical answer [src] 
0.0529587100712407
0.0529587100712407

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

    © Mister Exam – Calculator