Mister Exam

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Identical expressions
x^(one / two)-x^ two
x to the power of (1 divide by 2) minus x squared
x to the power of (one divide by two) minus x to the power of two
x(1/2)-x2
x1/2-x2
x^(1/2)-x²
x to the power of (1/2)-x to the power of 2
x^1/2-x^2
x^(1 divide by 2)-x^2
x^(1/2)-x^2dx
Similar expressions
x^(1/2)+x^2
x^1/2-x^2

Solving integrals/ x^(1/2)-x^2

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

The solution

You have entered [src]

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

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

Integral(sqrt(x) - x^2, (x, 0, 1))

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$$\frac{1}{3}$$

1/3

$$\frac{1}{3}$$

Упростить

Numerical answer [src]

0.333333333333333

0.333333333333333

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution