Mister Exam

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Identical expressions
one /4sqrtx/
1 divide by 4 square root of x divide by
one divide by 4 square root of x divide by
1/4√x/
1 divide by 4sqrtx divide by
1/4sqrtx/dx

Integral of 1/4sqrtx/ dx

The solution

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  1         
  /         
 |          
 |    ___   
 |  \/ x    
 |  ----- dx
 |    4     
 |          
/           
0

$$\int\limits_{0}^{1} \frac{\sqrt{x}}{4}\, dx$$

Integral(sqrt(x)/4, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\sqrt{x}}{4}\, dx = \frac{\int \sqrt{x}\, dx}{4}$
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: $\frac{x^{\frac{3}{2}}}{6}$
Add the constant of integration:

$\frac{x^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{\frac{3}{2}}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   
 |                    
 |   ___           3/2
 | \/ x           x   
 | ----- dx = C + ----
 |   4             6  
 |                    
/

$$\int \frac{\sqrt{x}}{4}\, dx = C + \frac{x^{\frac{3}{2}}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/6

$$\frac{1}{6}$$

1/6

$$\frac{1}{6}$$

1/6

Numerical answer [src]

0.166666666666667

0.166666666666667

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

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Identical expressions

Integral of 1/4sqrtx/ dx

Limits of integration:

The graph:

Piecewise:

The solution