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Solving integrals/ x^2-y

Integral of x^2-y dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    3           
 2*x            
   /            
  |             
  |  / 2    \   
  |  \x  - y/ dy
  |             
 /              
 0
$$\int\limits_{0}^{2 x^{3}} \left(x^{2} - y\right)\, dy$$ 
Integral(x^2 - y, (y, 0, 2*x^3))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    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:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                           
 |                    2       
 | / 2    \          y       2
 | \x  - y/ dy = C - -- + y*x 
 |                   2        
/
$$\int \left(x^{2} - y\right)\, dy = C + x^{2} y - \frac{y^{2}}{2}$$
Simplify
The answer [src] 
     6      5
- 2*x  + 2*x
$$- 2 x^{6} + 2 x^{5}$$ 
=
= 
     6      5
- 2*x  + 2*x
$$- 2 x^{6} + 2 x^{5}$$ 
-2*x^6 + 2*x^5

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

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