Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*e^(4*x)
Integral of x/sqrt(x^2-4x+1)
Integral of x/(x^2-1)^3
Integral of x*dx
Identical expressions
(- one)/sqrt(y)
( minus 1) divide by square root of (y)
( minus one) divide by square root of (y)
(-1)/√(y)
-1/sqrty
(-1) divide by sqrt(y)
Similar expressions
(y-1)/(sqrty+1)
(1)/sqrt(y)

Integral of (-1)/sqrt(y) dx

The solution

You have entered [src]

  1         
  /         
 |          
 |   -1     
 |  ----- dy
 |    ___   
 |  \/ y    
 |          
/           
0

$$\int\limits_{0}^{1} \left(- \frac{1}{\sqrt{y}}\right)\, dy$$

Integral(-1/sqrt(y), (y, 0, 1))

Detail solution

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

$\int \left(- \frac{1}{\sqrt{y}}\right)\, dy = - \int \frac{1}{\sqrt{y}}\, dy$
1. Let $u = \sqrt{y}$ .
  
  Then let $du = \frac{dy}{2 \sqrt{y}}$ and substitute $2 du$ :
  
  $\int 2\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $2 u$
  Now substitute $u$ back in:
  
  $2 \sqrt{y}$
So, the result is: $- 2 \sqrt{y}$
Add the constant of integration:

$- 2 \sqrt{y}+ \mathrm{constant}$

The answer is:

$- 2 \sqrt{y}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |  -1                ___
 | ----- dy = C - 2*\/ y 
 |   ___                 
 | \/ y                  
 |                       
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2

$$-2$$

-2

$$-2$$

-2

Numerical answer [src]

-1.99999999946942

-1.99999999946942

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(y) dx

Limits of integration:

The graph:

Piecewise:

The solution