Integral of x²+y² dx

The solution

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  1             
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 |  / 2    2\   
 |  \x  + y / dx
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0

$$\int\limits_{0}^{1} \left(x^{2} + y^{2}\right)\, dx$$

Integral(x^2 + y^2, (x, 0, 1))

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:
  
  $\int y^{2}\, dx = x y^{2}$
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]

1    2
- + y 
3

$$y^{2} + \frac{1}{3}$$

1    2
- + y 
3

$$y^{2} + \frac{1}{3}$$

1/3 + y^2

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

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Integral of x²+y² dx

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