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Identical expressions
one /sqrt4-3x^(two)
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one divide by square root of 4 minus 3x to the power of (two)
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1/sqrt4-3x^(2)dx
Similar expressions
1/sqrt4+3x^(2)

Integral of 1/sqrt4-3x^(2) dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |  /  1        2\   
 |  |----- - 3*x | dx
 |  |  ___       |   
 |  \\/ 4        /   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(- 3 x^{2} + \frac{1}{\sqrt{4}}\right)\, dx$$

Integral(1/(sqrt(4)) - 3*x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x^{2}\right)\, dx = - 3 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{1}{\sqrt{4}}\, dx = \frac{x}{2}$
The result is: $- x^{3} + \frac{x}{2}$
Add the constant of integration:

$- x^{3} + \frac{x}{2}+ \mathrm{constant}$

The answer is:

$- x^{3} + \frac{x}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 | /  1        2\          x    3
 | |----- - 3*x | dx = C + - - x 
 | |  ___       |          2     
 | \\/ 4        /                
 |                               
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2

$$- \frac{1}{2}$$

-1/2

$$- \frac{1}{2}$$

-1/2

Numerical answer [src]

-0.5

-0.5

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

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Integral of 1/sqrt4-3x^(2) dx

Limits of integration:

The graph:

Piecewise:

The solution