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Solving integrals/ (x^5-x^6)

Integral of (x^5-x^6) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |  / 5    6\   
 |  \x  - x / dx
 |              
/               
0
$$\int\limits_{0}^{1} \left(- x^{6} + x^{5}\right)\, dx$$ 
Integral(x^5 - x^6, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of is when :

      So, the result is:

    1. The integral of is when :

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                     7    6
 | / 5    6\          x    x 
 | \x  - x / dx = C - -- + --
 |                    7    6 
/
$$\int \left(- x^{6} + x^{5}\right)\, dx = C - \frac{x^{7}}{7} + \frac{x^{6}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1/42
$$\frac{1}{42}$$ 
=
= 
1/42
$$\frac{1}{42}$$ 
1/42
Numerical answer [src] 
0.0238095238095238
0.0238095238095238

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

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