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Solving integrals/ 1-x^3/y^3

Integral of 1-x^3/y^3 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  /     3\   
 |  |    x |   
 |  |1 - --| dx
 |  |     3|   
 |  \    y /   
 |             
/              
0
$$\int\limits_{0}^{1} \left(- \frac{x^{3}}{y^{3}} + 1\right)\, dx$$ 
Integral(1 - x^3/y^3, (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 a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                           
 | /     3\                4 
 | |    x |               x  
 | |1 - --| dx = C + x - ----
 | |     3|                 3
 | \    y /              4*y 
 |                           
/
$$\int \left(- \frac{x^{3}}{y^{3}} + 1\right)\, dx = C - \frac{x^{4}}{4 y^{3}} + x$$
Simplify
The answer [src] 
     1  
1 - ----
       3
    4*y
$$1 - \frac{1}{4 y^{3}}$$ 
=
= 
     1  
1 - ----
       3
    4*y
$$1 - \frac{1}{4 y^{3}}$$ 
1 - 1/(4*y^3)

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

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