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Integral of (x^2-y^2) dx

The solution

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  2             
  /             
 |              
 |  / 2    2\   
 |  \x  - y / dx
 |              
/               
1

$$\int\limits_{1}^{2} \left(x^{2} - y^{2}\right)\, dx$$

Integral(x^2 - y^2, (x, 1, 2))

Detail solution

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

$x \left(\frac{x^{2}}{3} - y^{2}\right)$
Add the constant of integration:

$x \left(\frac{x^{2}}{3} - y^{2}\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{2}}{3} - y^{2}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

7    2
- - y 
3

$$\frac{7}{3} - y^{2}$$

7    2
- - y 
3

$$\frac{7}{3} - y^{2}$$

7/3 - y^2

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

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Integral of (x^2-y^2) dx

Limits of integration:

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The solution