Mister Exam

Other calculators

Solving integrals/ x^2+y^2dx

Integral of x^2+y^2dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |  / 2    2  \   
 |  \x  + y *1/ dx
 |                
/                 
0
∫01(x2+y2⋅1) dx\int\limits_{0}^{1} \left(x^{2} + y^{2} \cdot 1\right)\, dx 
Integral(x^2 + y^2*1, (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⋅1 dx=xy2\int y^{2} \cdot 1\, 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 *1/ dx = C + -- + x*y 
 |                      3        
/
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}
Упростить

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

    © Mister Exam – Calculator