Mister Exam

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Integral of d{x}:
Integral of cosx
Integral of ln|x|
Integral of x*sin(x)^2
Integral of x^n*e^(-x)
Identical expressions
(- one / two)*(x^(- one / two))
( minus 1 divide by 2) multiply by (x to the power of ( minus 1 divide by 2))
( minus one divide by two) multiply by (x to the power of ( minus one divide by two))
(-1/2)*(x(-1/2))
-1/2*x-1/2
(-1/2)(x^(-1/2))
(-1/2)(x(-1/2))
-1/2x-1/2
-1/2x^-1/2
(-1 divide by 2)*(x^(-1 divide by 2))
(-1/2)*(x^(-1/2))dx
Similar expressions
(-1/2)*(x^(1/2))
(1/2)*(x^(-1/2))

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

The solution

You have entered [src]

  1           
  /           
 |            
 |    -1      
 |  ------- dx
 |      ___   
 |  2*\/ x    
 |            
/             
0

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

Integral(-1/(2*sqrt(x)), (x, 0, 1))

Detail solution

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

$\int \left(- \frac{1}{2 \sqrt{x}}\right)\, dx = - \frac{\int \frac{1}{\sqrt{x}}\, dx}{2}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{\sqrt{x}}\, dx = 2 \sqrt{x}$
So, the result is: $- \sqrt{x}$
Add the constant of integration:

$- \sqrt{x}+ \mathrm{constant}$

The answer is:

$- \sqrt{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |   -1               ___
 | ------- dx = C - \/ x 
 |     ___               
 | 2*\/ x                
 |                       
/

$$\int \left(- \frac{1}{2 \sqrt{x}}\right)\, dx = C - \sqrt{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1

$$-1$$

-1

$$-1$$

-1

Numerical answer [src]

-0.999999999734709

-0.999999999734709

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution