Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 5/x
Integral of x^1/3
Integral of ln^2(x)
Integral of exp(-x)
Canonical form:
x^2+y^2
Plot:
x^2+y^2
Inequation:
x^2+y^2
Identical expressions
x^ two +y^ two
x squared plus y squared
x to the power of two plus y to the power of two
x2+y2
x²+y²
x to the power of 2+y to the power of 2
x^2+y^2dx
Similar expressions
(x+y)/(1+x^(2)+y^(2))
2x+5+(2xy/(x^2+y^2))
x^2-y^2
x^2+y^2dx

Integral of x^2+y^2 dx

The solution

You have entered [src]

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

$$x\,y^2+{{x^3}\over{3}}$$

Simplify

The answer [src]

1    2
- + y 
3

$${{3\,y^2+1}\over{3}}$$

1    2
- + y 
3

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

Simplify

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x^2+y^2 dx

Limits of integration:

The graph:

Piecewise:

The solution