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Derivative of:
(1-x^2)^2
Limit of the function:
(1-x^2)^2
Identical expressions
(one -x^ two)^ two
(1 minus x squared ) squared
(one minus x to the power of two) to the power of two
(1-x2)2
1-x22
(1-x²)²
(1-x to the power of 2) to the power of 2
1-x^2^2
(1-x^2)^2dx
Similar expressions
(1+x^2)^2

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

The solution

You have entered [src]

 1/20            
   /             
  |              
  |          2   
  |  /     2\    
  |  \1 - x /  dx
  |              
 /               
 0

$$\int\limits_{0}^{\frac{1}{20}} \left(1 - x^{2}\right)^{2}\, dx$$

Integral((1 - x^2)^2, (x, 0, 1/20))

Detail solution

Rewrite the integrand:

$\left(1 - x^{2}\right)^{2} = x^{4} - 2 x^{2} + 1$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
  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: $- \frac{2 x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x$
Add the constant of integration:

$\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                 
 |         2                 3    5
 | /     2\               2*x    x 
 | \1 - x /  dx = C + x - ---- + --
 |                         3     5 
/

$$\int \left(1 - x^{2}\right)^{2}\, dx = C + \frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

2396003 
--------
48000000

$$\frac{2396003}{48000000}$$

2396003 
--------
48000000

$$\frac{2396003}{48000000}$$

2396003/48000000

Numerical answer [src]

0.0499167291666667

0.0499167291666667

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

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

Limits of integration:

The graph:

Piecewise:

The solution