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Integral of -1/3x^2+27
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Identical expressions
- one /3x^ two + twenty-seven
minus 1 divide by 3x squared plus 27
minus one divide by 3x to the power of two plus twenty minus seven
-1/3x2+27
-1/3x²+27
-1/3x to the power of 2+27
-1 divide by 3x^2+27
-1/3x^2+27dx
Similar expressions
-1/3x^2-27
1/3x^2+27

Solving integrals/ -1/3x^2+27

Integral of -1/3x^2+27 dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  /   2     \   
 |  |  x      |   
 |  |- -- + 27| dx
 |  \  3      /   
 |                
/                 
0

$$\int\limits_{0}^{1} \left(27 - \frac{x^{2}}{3}\right)\, dx$$

Integral(-x^2/3 + 27, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 27\, dx = 27 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{x^{2}}{3}\right)\, dx = - \frac{\int x^{2}\, dx}{3}$
  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: $- \frac{x^{3}}{9}$
The result is: $- \frac{x^{3}}{9} + 27 x$
Now simplify:

$\frac{x \left(243 - x^{2}\right)}{9}$
Add the constant of integration:

$\frac{x \left(243 - x^{2}\right)}{9}+ \mathrm{constant}$

The answer is:

$\frac{x \left(243 - x^{2}\right)}{9}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 | /   2     \                  3
 | |  x      |                 x 
 | |- -- + 27| dx = C + 27*x - --
 | \  3      /                 9 
 |                               
/

$$\int \left(27 - \frac{x^{2}}{3}\right)\, dx = C - \frac{x^{3}}{9} + 27 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

242/9

$$\frac{242}{9}$$

242/9

$$\frac{242}{9}$$

242/9

Numerical answer [src]

26.8888888888889

26.8888888888889

The graph

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

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Identical expressions

Similar expressions

Integral of -1/3x^2+27 dx

Limits of integration:

The graph:

Piecewise:

The solution