Mister Exam

Other calculators

Solving integrals/ x^(-0.5)*exp(-x)

Integral of x^(-0.5)*exp(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |    -x    
 |   e      
 |  ----- dx
 |    ___   
 |  \/ x    
 |          
/           
0
∫01e−xx dx\int\limits_{0}^{1} \frac{e^{- x}}{\sqrt{x}}\, dx 
Integral(exp(-x)/sqrt(x), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

    −πerfc⁡(x)+constant- \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}+ \mathrm{constant}

The answer is:

−πerfc⁡(x)+constant- \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                                  
 |   -x                             
 |  e               ____     /  ___\
 | ----- dx = C - \/ pi *erfc\\/ x /
 |   ___                            
 | \/ x                             
 |                                  
/
∫e−xx dx=C−πerfc⁡(x)\int \frac{e^{- x}}{\sqrt{x}}\, dx = C - \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900200
Plot the graph f(x)
The answer [src] 
  ____       
\/ pi *erf(1)
πerf⁡(1)\sqrt{\pi} \operatorname{erf}{\left(1 \right)} 
=
= 
  ____       
\/ pi *erf(1)
πerf⁡(1)\sqrt{\pi} \operatorname{erf}{\left(1 \right)} 
sqrt(pi)*erf(1)
Numerical answer [src] 
1.49364826509427
1.49364826509427

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

    © Mister Exam – Calculator