Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of exp(x)/x
Integral of x*exp(-x^2)
Integral of x/(x-1)^2
Integral of lnx^2
x^3*y^2
Identical expressions
x^ three *y^ two
x cubed multiply by y squared
x to the power of three multiply by y to the power of two
x3*y2
x³*y²
x to the power of 3*y to the power of 2
x^3y^2
x3y2
x^3*y^2dx

Solving integrals/ x^3*y^2

Integral of x^3*y^2 dx

The solution

You have entered [src]

  2         
  /         
 |          
 |   3  2   
 |  x *y  dx
 |          
/           
0

$$\int\limits_{0}^{2} x^{3} y^{2}\, dx$$

Integral(x^3*y^2, (x, 0, 2))

Detail solution

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

$\int x^{3} y^{2}\, dx = y^{2} \int x^{3}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
So, the result is: $\frac{x^{4} y^{2}}{4}$
Add the constant of integration:

$\frac{x^{4} y^{2}}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} y^{2}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                 4  2
 |  3  2          x *y 
 | x *y  dx = C + -----
 |                  4  
/

$$\int x^{3} y^{2}\, dx = C + \frac{x^{4} y^{2}}{4}$$

Simplify

The answer [src]

   2
4*y

$$4 y^{2}$$

=

   2
4*y

$$4 y^{2}$$

4*y^2

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