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Identical expressions
two *sqrt(x)- zero . two 5x^2
2 multiply by square root of (x) minus 0.25x squared
two multiply by square root of (x) minus zero . two 5x squared
2*√(x)-0.25x^2
2*sqrt(x)-0.25x2
2*sqrtx-0.25x2
2*sqrt(x)-0.25x²
2*sqrt(x)-0.25x to the power of 2
2sqrt(x)-0.25x^2
2sqrt(x)-0.25x2
2sqrtx-0.25x2
2sqrtx-0.25x^2
2*sqrt(x)-0.25x^2dx
Similar expressions
2*sqrt(x)+0.25x^2

Solving integrals/ 2*sqrt(x)-0.25x^2

Integral of 2*sqrt(x)-0.25x^2 dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sqrt{x}\, dx = 2 \int \sqrt{x}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
  So, the result is: $\frac{4 x^{\frac{3}{2}}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{x^{2}}{4}\right)\, dx = - \int \frac{x^{2}}{4}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{x^{2}}{4}\, dx = \frac{\int x^{2}\, dx}{4}$
    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: $\frac{x^{3}}{12}$
  So, the result is: $- \frac{x^{3}}{12}$
The result is: $\frac{4 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{12}$
Add the constant of integration:

$\frac{4 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{12}+ \mathrm{constant}$

The answer is:

$\frac{4 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 | /           2\           3      3/2
 | |    ___   x |          x    4*x   
 | |2*\/ x  - --| dx = C - -- + ------
 | \          4 /          12     3   
 |                                    
/

$${{4\,x^{{{3}\over{2}}}}\over{3}}-{{x^3}\over{12}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3

$${{16}\over{3}}$$

16/3

$$\frac{16}{3}$$

Simplify

Numerical answer [src]

5.33333333333333

5.33333333333333

The graph

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

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Integral of 2*sqrt(x)-0.25x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution