Mister Exam

Lang:

Solving integrals/ 2*sqrt(x)

Integral of 2*sqrt(x) dx

You have entered [src]

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

$$\int\limits_{0}^{1} 2 \sqrt{x}\, dx$$

Integral(2*sqrt(x), (x, 0, 1))

Detail solution

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: $\frac{4 x^{\frac{3}{2}}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$${{4}\over{3}}$$

4/3

$$\frac{4}{3}$$

Упростить

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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