Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(-1/2)
Integral of 1-7*x^2
Integral of y^(-2/3)
Integral of -xe^x
Identical expressions
-sqrt(4x+ one)
minus square root of (4x plus 1)
minus square root of (4x plus one)
-√(4x+1)
-sqrt4x+1
-sqrt(4x+1)dx
Similar expressions
-sqrt(4x-1)
sqrt(4x+1)

Integral of -sqrt(4x+1) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |     _________   
 |  -\/ 4*x + 1  dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \left(- \sqrt{4 x + 1}\right)\, dx$$

Integral(-sqrt(4*x + 1), (x, 0, 1))

Detail solution

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

$\int \left(- \sqrt{4 x + 1}\right)\, dx = - \int \sqrt{4 x + 1}\, dx$
1. Let $u = 4 x + 1$ .
  
  Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
  
  $\int \frac{\sqrt{u}}{4}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{4}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
    So, the result is: $\frac{u^{\frac{3}{2}}}{6}$
  Now substitute $u$ back in:
  
  $\frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}$
So, the result is: $- \frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}$
Now simplify:

$- \frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}$
Add the constant of integration:

$- \frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                                3/2
 |    _________          (4*x + 1)   
 | -\/ 4*x + 1  dx = C - ------------
 |                            6      
/

$$\int \left(- \sqrt{4 x + 1}\right)\, dx = C - \frac{\left(4 x + 1\right)^{\frac{3}{2}}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

        ___
1   5*\/ 5 
- - -------
6      6

$$\frac{1}{6} - \frac{5 \sqrt{5}}{6}$$

        ___
1   5*\/ 5 
- - -------
6      6

$$\frac{1}{6} - \frac{5 \sqrt{5}}{6}$$

1/6 - 5*sqrt(5)/6

Numerical answer [src]

-1.69672331458316

-1.69672331458316

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of -sqrt(4x+1) dx

Limits of integration:

The graph:

Piecewise:

The solution