Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (1/sqrt(2*pi))*exp((-x^2)/2)
Integral of e^(-x)cos(nx)
Integral of (x^3*cos(x/2)+1/2)*sqrt(4-x^2)
Integral of sin^4x/cos^6x
Identical expressions
(one /sqrt(two *pi))*exp((-x^ two)/ two)
(1 divide by square root of (2 multiply by Pi )) multiply by exponent of (( minus x squared ) divide by 2)
(one divide by square root of (two multiply by Pi )) multiply by exponent of (( minus x to the power of two) divide by two)
(1/√(2*pi))*exp((-x^2)/2)
(1/sqrt(2*pi))*exp((-x2)/2)
1/sqrt2*pi*exp-x2/2
(1/sqrt(2*pi))*exp((-x²)/2)
(1/sqrt(2*pi))*exp((-x to the power of 2)/2)
(1/sqrt(2pi))exp((-x^2)/2)
(1/sqrt(2pi))exp((-x2)/2)
1/sqrt2piexp-x2/2
1/sqrt2piexp-x^2/2
(1 divide by sqrt(2*pi))*exp((-x^2) divide by 2)
(1/sqrt(2*pi))*exp((-x^2)/2)dx
Similar expressions
(1/sqrt(2*pi))*exp((x^2)/2)

Solving integrals/ (1/sqrt(2*pi))*exp((-x^2)/2)

Integral of (1/sqrt(2pi))exp((-x^2)/2) dx

The solution

You have entered [src]

  x                    
  /                    
 |                     
 |                2    
 |              -x     
 |              ----   
 |       1       2     
 |  1*--------*e     dx
 |      ______         
 |    \/ 2*pi          
 |                     
/                      
0

$$\int\limits_{0}^{x} 1 \cdot \frac{1}{\sqrt{2 \pi}} e^{\frac{\left(-1\right) x^{2}}{2}}\, dx$$

Simplify

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 1 \cdot \frac{1}{\sqrt{2 \pi}} e^{\frac{\left(-1\right) x^{2}}{2}}\, dx = \frac{\sqrt{2}}{2 \sqrt{\pi}} \int e^{\frac{\left(-1\right) x^{2}}{2}}\, dx$
So, the result is: $\frac{\sqrt{2} \sqrt{\pi} \frac{\sqrt{2}}{2 \sqrt{\pi}} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$
Now simplify:

$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$
Add the constant of integration:

$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                            
 |                                           ___      /    ___\
 |               2             ___   ____  \/ 2       |x*\/ 2 |
 |             -x            \/ 2 *\/ pi *--------*erf|-------|
 |             ----                           ____    \   2   /
 |      1       2                         2*\/ pi              
 | 1*--------*e     dx = C + ----------------------------------
 |     ______                                2                 
 |   \/ 2*pi                                                   
 |                                                             
/

$${{\sqrt{\pi}\,\mathrm{erf}\left({{x}\over{\sqrt{2}}}\right)}\over{2 \,\sqrt{\pi}}}$$

Simplify

The answer [src]

   /    ___\
   |x*\/ 2 |
erf|-------|
   \   2   /
------------
     2

$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$

   /    ___\
   |x*\/ 2 |
erf|-------|
   \   2   /
------------
     2

$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$

Simplify

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (1/sqrt(2pi))exp((-x^2)/2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (1/sqrt(2*pi))*exp((-x^2)/2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of (1/sqrt(2pi))exp((-x^2)/2) dx