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Limit of the function:
x^(3/2)-x^2
Identical expressions
x^(three / two)-x^ two
x to the power of (3 divide by 2) minus x squared
x to the power of (three divide by two) minus x to the power of two
x(3/2)-x2
x3/2-x2
x^(3/2)-x²
x to the power of (3/2)-x to the power of 2
x^3/2-x^2
x^(3 divide by 2)-x^2
x^(3/2)-x^2dx
Similar expressions
x^(3/2)+x^2

Solving integrals/ x^(3/2)-x^2

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

The solution

You have entered [src]

  1               
  /               
 |                
 |  / 3/2    2\   
 |  \x    - x / dx
 |                
/                 
0

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

Integral(x^(3/2) - 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 $n \neq -1$ :
  
  $\int x^{\frac{3}{2}}\, dx = \frac{2 x^{\frac{5}{2}}}{5}$
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: $\frac{2 x^{\frac{5}{2}}}{5} - \frac{x^{3}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{2\,x^{{{5}\over{2}}}}\over{5}}-{{x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/15

$${{1}\over{15}}$$

1/15

$$\frac{1}{15}$$

Simplify

Numerical answer [src]

0.0666666666666667

0.0666666666666667

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution