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2(x^2+y^2)
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two (x^ two +y^ two)
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Similar expressions
2(x^2-y^2)

Integral of 2(x^2+y^2) dy

The solution

You have entered [src]

    ________              
   /      2               
 \/  4 - x                
      /                   
     |                    
     |        / 2    2\   
     |      2*\x  + y / dy
     |                    
    /                     
    0

$$\int\limits_{0}^{\sqrt{4 - x^{2}}} 2 \left(x^{2} + y^{2}\right)\, dy$$

Integral(2*(x^2 + y^2), (y, 0, sqrt(4 - x^2)))

Detail solution

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

          3/2                   
  /     2\              ________
2*\4 - x /         2   /      2 
------------- + 2*x *\/  4 - x  
      3

$$2 x^{2} \sqrt{4 - x^{2}} + \frac{2 \left(4 - x^{2}\right)^{\frac{3}{2}}}{3}$$

          3/2                   
  /     2\              ________
2*\4 - x /         2   /      2 
------------- + 2*x *\/  4 - x  
      3

$$2 x^{2} \sqrt{4 - x^{2}} + \frac{2 \left(4 - x^{2}\right)^{\frac{3}{2}}}{3}$$

2*(4 - x^2)^(3/2)/3 + 2*x^2*sqrt(4 - x^2)

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

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Integral of 2(x^2+y^2) dy

Limits of integration:

The graph:

Piecewise:

The solution