Mister Exam

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Graphing y =:
-x^3+3*x
Derivative of:
-x^3+3*x
Limit of the function:
-x^3+3*x
Identical expressions
-x^ three + three *x
minus x cubed plus 3 multiply by x
minus x to the power of three plus three multiply by x
-x3+3*x
-x³+3*x
-x to the power of 3+3*x
-x^3+3x
-x3+3x
-x^3+3*xdx
Similar expressions
x^3+3*x
-x^3-3*x

Integral of -x^3+3*x dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |  /   3      \   
 |  \- x  + 3*x/ dx
 |                 
/                  
0

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/4

$$\frac{5}{4}$$

5/4

$$\frac{5}{4}$$

5/4

Numerical answer [src]

1.25

1.25

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

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Identical expressions

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Integral of -x^3+3*x dx

Limits of integration:

The graph:

Piecewise:

The solution