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Solving integrals/ x^2+y^2

Integral of x^2+y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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0
∫01(x2+y2) dx\int\limits_{0}^{1} \left(x^{2} + y^{2}\right)\, dx 
Integral(x^2 + y^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

      ∫y2 dx=xy2\int y^{2}\, dx = x y^{2}

    The result is: x33+xy2\frac{x^{3}}{3} + x y^{2}

  2. Now simplify:

    x(x23+y2)x \left(\frac{x^{2}}{3} + y^{2}\right)

  3. Add the constant of integration:

    x(x23+y2)+constantx \left(\frac{x^{2}}{3} + y^{2}\right)+ \mathrm{constant}

The answer is:

x(x23+y2)+constantx \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 
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/
x y2+x33x\,y^2+{{x^3}\over{3}}
Simplify
The answer [src] 
1    2
- + y 
3
3 y2+13{{3\,y^2+1}\over{3}} 
=
= 
1    2
- + y 
3
y2+13y^{2} + \frac{1}{3}
Simplify

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

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