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Integral of d{x}:
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Integral of -x^3
Canonical form:
4x^2-x^4
Graphing y =:
4x^2-x^4
Identical expressions
four x^ two -x^4
4x squared minus x to the power of 4
four x to the power of two minus x to the power of 4
4x2-x4
4x²-x⁴
4x to the power of 2-x to the power of 4
4x^2-x^4dx
Similar expressions
4x^2+x^4

Solving integrals/ 4x^2-x^4

Integral of 4x^2-x^4 dx

The solution

You have entered [src]

  2               
  /               
 |                
 |  /   2    4\   
 |  \4*x  - x / dx
 |                
/                 
0

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

Integral(4*x^2 - x^4, (x, 0, 2))

Detail solution

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

$\frac{x^{3} \left(20 - 3 x^{2}\right)}{15}$
Add the constant of integration:

$\frac{x^{3} \left(20 - 3 x^{2}\right)}{15}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(20 - 3 x^{2}\right)}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                       5      3
 | /   2    4\          x    4*x 
 | \4*x  - x / dx = C - -- + ----
 |                      5     3  
/

$$\int \left(- x^{4} + 4 x^{2}\right)\, dx = C - \frac{x^{5}}{5} + \frac{4 x^{3}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

64
--
15

$$\frac{64}{15}$$

64
--
15

$$\frac{64}{15}$$

64/15

Numerical answer [src]

4.26666666666667

4.26666666666667

The graph

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

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Identical expressions

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Integral of 4x^2-x^4 dx

Limits of integration:

The graph:

Piecewise:

The solution