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Derivative of:
3sqrtx^2
Identical expressions
3sqrtx^ two
3 square root of x squared
3 square root of x to the power of two
3√x^2
3sqrtx2
3sqrtx²
3sqrtx to the power of 2
3sqrtx^2dx

Integral of 3sqrtx^2 dx

The solution

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  8            
  /            
 |             
 |         2   
 |      ___    
 |  3*\/ x   dx
 |             
/              
1

$$\int\limits_{1}^{8} 3 \left(\sqrt{x}\right)^{2}\, dx$$

Integral(3*(sqrt(x))^2, (x, 1, 8))

Detail solution

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

$\int 3 \left(\sqrt{x}\right)^{2}\, dx = 3 \int \left(\sqrt{x}\right)^{2}\, dx$
1. Let $u = \sqrt{x}$ .
  
  Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$ :
  
  $\int 2 u^{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u^{3}\, du = 2 \int u^{3}\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{3}\, du = \frac{u^{4}}{4}$
    So, the result is: $\frac{u^{4}}{2}$
  Now substitute $u$ back in:
  
  $\frac{x^{2}}{2}$
So, the result is: $\frac{3 x^{2}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int 3 \left(\sqrt{x}\right)^{2}\, dx = C + \frac{3 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

189/2

$$\frac{189}{2}$$

189/2

$$\frac{189}{2}$$

189/2

Numerical answer [src]

94.5

94.5

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

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Identical expressions

Integral of 3sqrtx^2 dx

Limits of integration:

The graph:

Piecewise:

The solution