Integral of 4*sqrt(x) dx

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  4           
  /           
 |            
 |      ___   
 |  4*\/ x  dx
 |            
/             
1

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

Integral(4*sqrt(x), (x, 1, 4))

Detail solution

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

$\int 4 \sqrt{x}\, dx = 4 \int \sqrt{x}\, dx$
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: $\frac{8 x^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{8 x^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{8 x^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                     3/2
 |     ___          8*x   
 | 4*\/ x  dx = C + ------
 |                    3   
/

$$\int 4 \sqrt{x}\, dx = C + \frac{8 x^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

56/3

$$\frac{56}{3}$$

56/3

$$\frac{56}{3}$$

56/3

Numerical answer [src]

18.6666666666667

18.6666666666667

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