Mister Exam

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How to use it?
Integral of d{x}:
Integral of exp(4*x)
Integral of x*sin(2*x)
Integral of 1/(x^2+2*x)
Integral of cos(x)*exp(x)
x^2*y^2
The double integral of:
x^2*y^2
Limit of the function:
x^2*y^2
Identical expressions
x^ two *y^ two
x squared multiply by y squared
x to the power of two multiply by y to the power of two
x2*y2
x²*y²
x to the power of 2*y to the power of 2
x^2y^2
x2y2
x^2*y^2dx

Solving integrals/ x^2*y^2

Integral of x^2*y^2 dx

The solution

You have entered [src]

  1         
  /         
 |          
 |   2  2   
 |  x *y  dx
 |          
/           
0

\int\limits_{0}^{1} x^{2} y^{2}\, dx

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

Detail solution

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

$\int x^{2} y^{2}\, dx = y^{2} \int x^{2}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
So, the result is: $\frac{x^{3} y^{2}}{3}$
Add the constant of integration:

$\frac{x^{3} y^{2}}{3}+ \mathrm{constant}$

The answer is:

\frac{x^{3} y^{2}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                    
 |                 3  2
 |  2  2          x *y 
 | x *y  dx = C + -----
 |                  3  
/

\int x^{2} y^{2}\, dx = C + \frac{x^{3} y^{2}}{3}

Simplify

The answer [src]

 2
y 
--
3

\frac{y^{2}}{3}

=

 2
y 
--
3

\frac{y^{2}}{3}

y^2/3

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